Douglas P. Hardin

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All published works

Action	Title	Year	Authors
+	Energy bounds for weighted spherical codes and designs via linear programming	2025	Sergiy Borodachov Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+	Universal minima of discrete potentials for sharp spherical codes	2024	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+ PDF Chat	Bounds on energy and potentials of discrete measures on the sphere	2024	Sergiy Borodachov Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin E. B. Saff Maya Stoyanova
+ PDF Chat	Energy bounds for weighted spherical codes and designs via linear programming	2024	Sergiy V. Borodachov Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+ PDF Chat	Asymptotics of k-nearest Neighbor Riesz Energies	2023	Douglas P. Hardin Edward B. Saff Oleksandr Vlasiuk
+ PDF Chat	On polarization of spherical codes and designs	2023	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+	Universally Optimal Periodic Configurations in the Plane	2023	Douglas P. Hardin Nathaniel Tenpas
+	Corrigendum to “Asymptotics for the Unconstrained Polarization (Chebyshev) Problem”	2022	Douglas P. Hardin Mircea Petrache Edward B. Saff
+	Asymptotics of $k$-nearest neighbor Riesz energies	2022	Douglas P. Hardin Edward B. Saff Oleksandr Vlasiuk
+	On polarization of spherical codes and designs	2022	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+	Universal minima of discrete potentials for sharp spherical codes	2022	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+ PDF Chat	Eigenfunctions of the Fourier transform with specified zeros	2021	Ahram S. Feigenbaum Peter J. Grabner Douglas P. Hardin
+ PDF Chat	Universal Bounds for Size and Energy of Codes of Given Minimum and Maximum Distances	2021	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+	Bounds for spherical codes: The Levenshtein framework lifted	2021	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin E. B. Saff Maya Stoyanova
+ PDF Chat	Dynamics of particles on a curve with pairwise hyper-singular repulsion	2021	Douglas P. Hardin Edward B. Saff Ruiwen Shu Eitan Tadmor
+ PDF Chat	Inverse potential problems in divergence form for measures in the plane	2021	Laurent Baratchart Cristóbal Villalobos Guillén Douglas P. Hardin
+	An Application of Coxeter Groups to the Construction of Wavelet Bases in Rn	2020	Jeffrey S. Geronimo Douglas P. Hardin Peter Massopust
+ PDF Chat	On the Search for Tight Frames of Low Coherence	2020	Xuemei Chen Douglas P. Hardin Edward B. Saff
+	Dynamics of Particles on a Curve with Pairwise Hyper-singular Repulsion	2020	Douglas P. Hardin Edward B. Saff Ruiwen Shu Eitan Tadmor
+ PDF Chat	Unconstrained Polarization (Chebyshev) Problems: Basic Properties and Riesz Kernel Asymptotics	2020	Douglas P. Hardin Mircea Petrache Edward B. Saff
+ PDF Chat	Hyperuniform point sets on the sphere: probabilistic aspects	2020	Ahram S. Feigenbaum Peter J. Grabner Douglas P. Hardin
+ PDF Chat	Divergence-Free Measures in the Plane and Inverse Potential Problems in Divergence Form	2020	Laurent Baratchart Cristóbal Villalobos Guillén Douglas P. Hardin
+	Sparse recovery for inverse potential problems in divergence form	2020	Laurent Baratchart Cristobal Villalobos-Guillen Douglas P. Hardin Juliette Leblond
+ PDF Chat	Constrained minimum Riesz energy problems for a condenser with intersecting plates	2020	Peter D Dragnev Bent Fuglede Douglas P. Hardin Edward B. Saff Natalia Zorii
+ PDF Chat	Upper bounds for energies of spherical codes of given cardinality and separation	2020	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+	On the Search for Tight Frames of Low Coherence	2020	Xuemei Chen Douglas P. Hardin Edward B. Saff
+	Divergence-free measures in the plane and inverse potential problems in divergence form	2020	Laurent Baratchart Cristóbal Villalobos Guillén Douglas P. Hardin
+	Asymptotic properties of short-range interaction functionals	2020	Douglas P. Hardin Edward B. Saff Oleksandr Vlasiuk
+	Dynamics of Particles on a Curve with Pairwise Hyper-singular Repulsion	2020	Douglas P. Hardin Edward B. Saff Ruiwen Shu Eitan Tadmor
+ PDF Chat	Inverse Potential Problems for Divergence of Measures with Total Variation Regularization	2019	Laurent Baratchart Cristóbal Villalobos Guillén Douglas P. Hardin Michael Northington Edward B. Saff
+	On Two Problems Concerning Universal Bounds for Codes	2019	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+	Linear Programming Bounds for Cardinality and Energy of Codes of Given Min and Max Distances	2019	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+ PDF Chat	Energy bounds for codes in polynomial metric spaces	2019	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+	Unconstrained polarization (Chebyshev) problems: basic properties and Riesz kernel asymptotics	2019	Douglas P. Hardin Mircea Petrache Edward B. Saff
+ PDF Chat	Condensers with Touching Plates and Constrained Minimum Riesz and Green Energy Problems	2019	Peter D Dragnev Bent Fuglede Douglas P. Hardin Edward B. Saff Natalia Zorii
+	Universal bounds for spherical codes: the Levenshtein framework lifted	2019	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+	Upper bounds for energies of spherical codes of given cardinality and separation	2019	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+	Universal Bounds for Size and Energy of Codes of Given Minimum and Maximum Distances	2019	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+	Minimal Energy Asymptotics in the “Harmonic Series” Case	2019	Sergiy Borodachov Douglas P. Hardin Edward B. Saff
+	Linear Programming Bounds and Universal Optimality on the Sphere	2019	Sergiy Borodachov Douglas P. Hardin Edward B. Saff
+	Some Popular Algorithms for Distributing Points on $$S^2$$	2019	Sergiy Borodachov Douglas P. Hardin Edward B. Saff
+	Best-Packing on Compact Sets	2019	Sergiy Borodachov Douglas P. Hardin Edward B. Saff
+	Asymptotics for Energy Minimizing Configurations on $$S^d$$	2019	Sergiy Borodachov Douglas P. Hardin Edward B. Saff
+	Configurations with Nonuniform Distribution	2019	Sergiy Borodachov Douglas P. Hardin Edward B. Saff
+	Minimal Energy in the Hypersingular Case	2019	Sergiy Borodachov Douglas P. Hardin Edward B. Saff
+	Introduction to Best-Packing and Best-Covering	2019	Sergiy Borodachov Douglas P. Hardin Edward B. Saff
+	Continuous Energy and Its Relation to Discrete Energy	2019	Sergiy Borodachov Douglas P. Hardin Edward B. Saff
+	An Overview: Discretizing Manifolds via Particle Interactions	2019	Sergiy Borodachov Douglas P. Hardin Edward B. Saff
+	Low-Complexity Energy Methods for Discretization	2019	Sergiy Borodachov Douglas P. Hardin Edward B. Saff
+	Periodic Riesz and Gauss-Type Potentials	2019	Sergiy Borodachov Douglas P. Hardin Edward B. Saff
+	Basic Properties and Examples of Minimal Discrete Energy	2019	Sergiy Borodachov Douglas P. Hardin Edward B. Saff
+	Optimal Discrete Measures for Potentials: Polarization (Chebyshev) Constants	2019	Sergiy Borodachov Douglas P. Hardin Edward B. Saff
+	Unconstrained polarization (Chebyshev) problems: basic properties and Riesz kernel asymptotics	2019	Douglas P. Hardin Mircea Petrache Edward B. Saff
+ PDF Chat	Magnetic moment estimation and bounded extremal problems	2018	Laurent Baratchart Sylvain Chevillard Douglas P. Hardin Juliette Leblond Eduardo A. Lima Jean-Paul Marmorat
+ PDF Chat	ASYMPTOTIC LINEAR PROGRAMMING LOWER BOUNDS FOR THE ENERGY OF MINIMIZING RIESZ AND GAUSS CONFIGURATIONS	2018	Douglas P. Hardin T. J. Michaels Edward B. Saff
+	Inverse Potential Problems for Divergence of Measures with Total Variation Regularization	2018	Laurent Baratchart Cristóbal Villalobos Guillén Douglas P. Hardin Michael Northington Edward B. Saff
+ PDF Chat	On spherical codes with inner products in a prescribed interval	2018	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+ PDF Chat	Large Deviation Principles for Hypersingular Riesz Gases	2018	Douglas P. Hardin Thomas Leblé Edward B. Saff Sylvia Serfaty
+	Optimal discrete measures for Riesz potentials	2018	Sergiy V. Borodachov Douglas P. Hardin Alexander Reznikov E. B. Saff
+	On spherical codes with inner products in a prescribed interval	2018	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+	Energy Bounds for Codes in Polynomial Metric Spaces	2018	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+	Inverse Potential Problems for Divergence of Measures with Total Variation Regularization	2018	Laurent Baratchart Cristóbal Villalobos Guillén Douglas P. Hardin Michael Northington Edward B. Saff
+ PDF Chat	Local Properties of Riesz Minimal Energy Configurations and Equilibrium Measures	2017	Douglas P. Hardin Alexander Reznikov Edward B. Saff Alexander Volberg
+ PDF Chat	Universal Lower Bounds on Energy and LP-Extremal Polynomials for (4, 24)-Codes	2017	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+	Local properties of Riesz minimal energy configurations and equilibrium measures	2017	Douglas P. Hardin Alexander Reznikov Edward B. Saff Alexander Volberg
+	Constrained minimum Riesz energy problems for a condenser with intersecting plates	2017	Peter D Dragnev Bent Fuglede Douglas P. Hardin Edward B. Saff Natalia Zorii
+	Condensers with touching plates and constrained minimum Riesz and Green energy problems	2017	Peter D Dragnev Bent Fuglede Douglas P. Hardin Edward B. Saff Natalia Zorii
+ PDF Chat	Generating Point Configurations via Hypersingular Riesz Energy with an External Field	2017	Douglas P. Hardin E. B. Saff Oleksandr Vlasiuk
+ PDF Chat	Energy bounds for codes and designs in Hamming spaces	2016	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+	Lower energy bounds for antipodal spherical codes and for codes in infinite projective spaces	2016	Peter Boyvalenkov Douglas P. Hardin Edward B. Saff Peter D Dragnev Maya Stoyanova
+ PDF Chat	Next Order Energy Asymptotics for Riesz Potentials on Flat Tori	2016	Douglas P. Hardin Edward B. Saff Brian Simanek Yujian Su
+	A sharp Balian–Low uncertainty principle for shift-invariant spaces	2016	Douglas P. Hardin Michael Northington Alexander M. Powell
+ PDF Chat	Universal Lower Bounds for Potential Energy of Spherical Codes	2016	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+	Generating Point Configurations via Hypersingular Riesz Energy With an External Field	2016	Douglas P. Hardin Edward B. Saff Oleksandr Vlasiuk
+	Optimal discrete measures for Riesz potentials	2016	Sergiy V. Borodachov Douglas P. Hardin Alexander Reznikov Edward B. Saff
+	A Comparison of Popular Point Configurations on $\mathbb{S}^2$	2016	Douglas P. Hardin T. J. Michaels Edward B. Saff
+	A Comparison of Popular Point Configurations on S^2	2016	Douglas P. Hardin T. J. Michaels Edward B. Saff
+ PDF Chat	Minimum Riesz Energy Problems for a Condenser with Touching Plates	2015	Peter D Dragnev Bent Fuglede Douglas P. Hardin Edward B. Saff Natalia Zorii
+	Universal upper and lower bounds on energy of spherical designs	2015	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+	Universal upper and lower bounds on energy of spherical designs	2015	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+	Next order energy asymptotics for Riesz potentials on flat tori	2015	Douglas P. Hardin Edward B. Saff Brian Simanek Yujian Su
+	Minimum Riesz energy problems for a condenser with "touching plates"	2015	Peter D Dragnev Douglas P. Hardin Edward B. Saff Natalia Zorii
+	Universal lower bounds for potential energy of spherical codes	2015	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova
+ PDF Chat	Wavelets Centered on a Knot Sequence: Theory, Construction, and Applications	2014	Bruce W. Anderson Derek O. Bruff Jeffrey S. Geronimo Douglas P. Hardin
+ PDF Chat	Periodic discrete energy for long-range potentials	2014	Douglas P. Hardin Edward B. Saff Brian Simanek
+ PDF Chat	INVERSE BERNSTEIN INEQUALITIES AND MIN–MAX–MIN PROBLEMS ON THE UNIT CIRCLE	2014	Tamás Erdélyi Douglas P. Hardin Edward B. Saff
+ PDF Chat	Low Complexity Methods For Discretizing Manifolds Via Riesz Energy Minimization	2014	Sergiy Borodachov Douglas P. Hardin Edward B. Saff
+	Minimal N -point diameters and f -best-packing constants in R d	2014	Andriy Bondarenko Douglas P. Hardin Edward B. Saff
+	Minimal 𝑁-point diameters and 𝑓-best-packing constants in ℝ^{𝕕}	2013	Andriy Bondarenko Douglas P. Hardin E. B. Saff
+ PDF Chat	Observed asymptotic differences in energies of stable and minimal point configurations on $\mathbb {S}^2$S2 and the role of defects	2013	Matthew T. Calef Whitney Griffiths Alexia Schulz C. Fichtl Douglas P. Hardin
+ PDF Chat	Mesh ratios for best-packing and limits of minimal energy configurations	2013	Andriy Bondarenko Douglas P. Hardin E. B. Saff
+	Asymptotic Differences in Energies of Stable and Minimal Point Configurations on S^2 and the Role of Defects	2013	Matthew T. Calef C. Fichtl Whitney C. Goulart Douglas P. Hardin Alexia Schulz
+ PDF Chat	Polarization Optimality of Equally Spaced Points on the Circle for Discrete Potentials	2013	Douglas P. Hardin Amos P. Kendall Edward B. Saff
+	Characterizing kernels of operators related to thin-plate magnetizations via generalizations of Hodge decompositions	2013	Laurent Baratchart Douglas P. Hardin Eduardo A. Lima E. B. Saff B. P. Weiss
+	Low complexity methods for discretizing manifolds via Riesz energy minimization	2013	Sergiy V. Borodachov Douglas P. Hardin Edward B. Saff
+ PDF Chat	Characterizing kernels of operators related to thin-plate magnetizations via generalizations of Hodge decompositions	2012	Laurent Baratchart Douglas P. Hardin Eduardo A. Lima E. B. Saff B. P. Weiss
+ PDF Chat	The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere	2012	Johann S. Brauchart Douglas P. Hardin Edward B. Saff
+ PDF Chat	Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications	2012	J. S. Brauchart Douglas P. Hardin E. B. Saff
+	Minimal $N$-Point Diameters and $f$-Best-Packing Constants in $R^d$	2012	Andriy Bondarenko Douglas P. Hardin Edward B. Saff
+	Mesh ratios for best-packing and limits of minimal energy configurations	2012	Andriy Bondarenko Douglas P. Hardin Edward B. Saff
+	Polarization optimality of equally spaced points on the circle for discrete potentials	2012	Douglas P. Hardin Amos P. Kendall Edward B. Saff
+	The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere	2012	J. Brauchart Douglas P. Hardin E. B. Saff
+	Quasi-uniformity of minimal weighted energy points on compact metric spaces	2011	Douglas P. Hardin Edward B. Saff J. Tyler Whitehouse
+	Wavelets centered on a knot sequence: theory, construction, and applications	2011	B. W. Atkinson Derek O. Bruff Jeffrey S. Geronimo Douglas P. Hardin
+	Discretizing Compact Manifolds with Minimum Energy	2011	Douglas P. Hardin
+	Quasi-uniformity of Minimal Weighted Energy Points on Compact Metric Spaces	2011	Douglas P. Hardin Edward B. Saff J. Tyler Whitehouse
+	Wavelets centered on a knot sequence: theory, construction, and applications	2011	B. W. Atkinson Derek Bruff Jeffrey S. Geronimo Douglas P. Hardin
+	New Results - Inverse problems for elliptic operators	2010	Laurent Baratchart Aline Bonami Slah Chaabi Maureen Clerc Yannick Fischer Sandrine Grellier Douglas P. Hardin Juliette Leblond Jean-Paul Marmorat Ana-Maria Nicu
+	Discrete Energy Asymptotics on a Riemannian circle	2009	Johann S. Brauchart Douglas P. Hardin Edward B. Saff
+ PDF Chat	The Riesz energy of the <i>N</i> th roots of unity: an asymptotic expansion for large <i>N</i>	2009	Johann S. Brauchart Douglas P. Hardin Edward B. Saff
+ PDF Chat	Riesz s-Equilibrium Measures on d-Rectifiable Sets as s Approaches d	2009	Matthew T. Calef Douglas P. Hardin
+	Discrete Minimum Energy Problems	2009	Douglas P. Hardin
+ PDF Chat	Riesz energy and sets of revolution in ℝ³	2009	Johann S. Brauchart Douglas P. Hardin Edward B. Saff
+	Asymptotics of weighted best-packing on rectifiable sets	2008	Sergiy Borodachov Douglas P. Hardin Edward B. Saff
+ PDF Chat	Асимптотика плотнейших взвешенных упаковок на спрямляемых множествах	2008	Sergiy V. Borodachov Sergiy V. Borodachov Эдвард Барри Сафф Edward B. Saff Д П Хардин Douglas P. Hardin
+	Riesz $s$-equilibrium measures on $d$-rectifiable sets as $s$ approaches $d$	2008	Matthew T. Calef Douglas P. Hardin
+ PDF Chat	The support of the limit distribution of optimal Riesz energy points on sets of revolution in R3	2007	Johann S. Brauchart Douglas P. Hardin Edward B. Saff
+ PDF Chat	Asymptotics for discrete weighted minimal Riesz energy problems on rectifiable sets	2007	Sergiy Borodachov Douglas P. Hardin Edward B. Saff
+	Optimal shift invariant spaces and their Parseval frame generators	2007	Akram Aldroubi Carlos Cabrelli Douglas P. Hardin Ursula Molter
+ PDF Chat	Asymptotics of best-packing on rectifiable sets	2007	Sergiy Borodachov Douglas P. Hardin Edward B. Saff
+ PDF Chat	Support of the logarithmic equilibrium measure on sets of revolution in R3	2007	Douglas P. Hardin Edward B. Saff Herbert Stahl
+	Minimum Riesz s-energy points on compact sets in R^3	2007	Johann S. Brauchart Douglas P. Hardin Edward B. Saff
+	Geometric measure theoretic approaches to potentials on fractales and manifolds.	2007	Peter J. Grabner Douglas P. Hardin Edward B. Saff Martina Zähle
+	Optimal Shift Invariant Spaces and Their Parseval Generators	2006	Akram Aldroubi Carlos Cabrelli Douglas P. Hardin Ursula Molter
+	Asymptotics for Discrete Weighted Minimal Riesz Energy Problems on Rectifiable Sets	2006	Sergiy V. Borodachov Douglas P. Hardin Edward B. Saff
+	Asymptotics of Best-Packing on Rectifiable Sets	2006	Sergiy V. Borodachov Douglas P. Hardin Edward B. Saff
+	Minimal Riesz energy point configurations for rectifiable <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>d</mml:mi></mml:math>-dimensional manifolds	2004	Douglas P. Hardin Edward B. Saff
+	None	2003	Douglas P. Hardin Thomas A. Hogan Qiyu Sun
+	Minimal Riesz Energy Point Configurations for Rectifiable d-Dimensional Manifolds	2003	Douglas P. Hardin Edward B. Saff
+	Wavelets are Piecewise Fractal Interpolation Functions	2002	Douglas P. Hardin
+	Multivariate nonhomogeneous refinement equations	1999	Thomas B. Dinsenbacher Douglas P. Hardin
+	Biorthogonal Multiwavelets on [−1, 1]	1999	Douglas P. Hardin Jeffrey A. Marasovich
+	Intertwining Multiresolution Analyses and the Construction of Piecewise-Polynomial Wavelets	1996	George C. Donovan Jeffrey S. Geronimo Douglas P. Hardin
+	<title>Construction of two-dimensional multiwavelets on a triangulation</title>	1996	George C. Donovan Jeffrey S. Geronimo Douglas P. Hardin William J. Kessler
+ PDF Chat	Construction of Orthogonal Wavelets Using Fractal Interpolation Functions	1996	George C. Donovan Jeffrey S. Geronimo Douglas P. Hardin Peter Massopust
+	Why and how prefiltering for discrete multiwavelet transforms	1996	Xiang‐Gen Xia Jeffrey S. Geronimo Douglas P. Hardin Bruce W. Suter
+	Design of prefilters for discrete multiwavelet transforms	1996	X.-G. Xia Jeffrey S. Geronimo Douglas P. Hardin Bruce W. Suter
+	<title>Computations of multiwavelet transforms</title>	1995	Xiang‐Gen Xia Jeffrey S. Geronimo Douglas P. Hardin Bruce W. Suter
+	<title>Fractal function, splines, intertwining multiresolution analysis, and wavelets</title>	1994	George C. Donovan Jeffrey S. Geronimo Douglas P. Hardin
+	Fractal Functions and Wavelet Expansions Based on Several Scaling Functions	1994	Jeffrey S. Geronimo Douglas P. Hardin Peter Massopust
+	Fractal Surfaces, Multiresolution Analyses and Wavelet Transforms	1994	Jeffrey S. Geronimo Douglas P. Hardin Peter Massopust
+ PDF Chat	Fractal Interpolation Functions from $R^n$ into $R^m$ and their Projections	1993	Douglas P. Hardin Peter Massopust
+	Fractal Interpolation Surfaces and a Related 2-D Multiresolution Analysis	1993	Jeffrey S. Geronimo Douglas P. Hardin
+	Multiresolution analyses based on fractal functions	1992	Douglas P. Hardin Bruce Kessler Peter Massopust
+	Dimensions associated with recurrent self-similar sets	1991	Anca Deliu Jeffrey S. Geronimo Ronald W. Shonkwiler Douglas P. Hardin
+	A Thousand Points of Light	1990	Douglas P. Hardin Gilbert Strang
+	Dispersion population models discrete in time and continuous in space	1990	Douglas P. Hardin Peter Takáč Glenn F. Webb
+	An exact formula for the measure dimensions associated with a class of piecewise linear maps	1989	Jeffrey S. Geronimo Douglas P. Hardin
+	Recurrent iterated function systems	1989	Michael F. Barnsley John H. Elton Douglas P. Hardin
+ PDF Chat	A Mandelbrot Set whose Boundary is Piecewise Smooth	1989	M. F. Barnsley Douglas P. Hardin
+	Hidden Variable Fractal Interpolation Functions	1989	Michael F. Barnsley John H. Elton Douglas P. Hardin Peter Massopust
+ PDF Chat	A Mandelbrot set whose boundary is piecewise smooth	1989	Michael F. Barnsley Douglas P. Hardin
+	Recurrent Iterated Function Systems	1989	Michael F. Barnsley John H. Elton Douglas P. Hardin
+	An Exact Formula for the Measure Dimensions Associated with a Class of Piecewise Linear Maps	1989	Jeffrey S. Geronimo Douglas P. Hardin
+	A Comparison of Dispersal Strategies for Survival of Spatially Heterogeneous Populations	1988	Douglas P. Hardin Peter Takáč Glenn F. Webb
+	Asymptotic properties of a continuous-space discrete-time population model in a random environment	1988	Douglas P. Hardin Peter Takáč Glenn F. Webb
+	The capacity for a class of fractal functions	1986	Douglas P. Hardin Peter Massopust
+	Solution of an inverse problem for fractals and other sets	1986	Michael F. Barnsley Vincent J. Ervin Douglas P. Hardin Jill Lancaster
+	Hyperbolic iterated function systems and applications	1985	Douglas P. Hardin
+	Solutions for Model Boltzmann Equations Proposed by Ziff	1984	Douglas P. Hardin James V. Herod

Common Coauthors

Coauthor	Papers Together
Edward B. Saff	98
Peter D Dragnev	32
Sergiy V. Borodachov	27
Peter Boyvalenkov	26
Maya Stoyanova	26
Jeffrey S. Geronimo	17
Laurent Baratchart	11
E. B. Saff	10
Peter Massopust	8
Cristóbal Villalobos Guillén	6
Natalia Zorii	6
Michael F. Barnsley	5
Bent Fuglede	5
Andriy Bondarenko	5
Oleksandr Vlasiuk	5
Johann S. Brauchart	5
Michael Northington	4
Matthew T. Calef	4
Mircea Petrache	4
Alexander Reznikov	4
George C. Donovan	4
Juliette Leblond	3
Peter J. Grabner	3
Bruce W. Suter	3
T. J. Michaels	3
Glenn F. Webb	3
Eitan Tadmor	3
John H. Elton	3
Brian Simanek	3
Eduardo A. Lima	3
Peter Takáč	3
Jean-Paul Marmorat	2
Derek O. Bruff	2
B. W. Atkinson	2
Akram Aldroubi	2
Xiang‐Gen Xia	2
Alexander Volberg	2
B. P. Weiss	2
C. Fichtl	2
Alexia Schulz	2
Carlos Cabrelli	2
J. Tyler Whitehouse	2
Ahram S. Feigenbaum	2
Xuemei Chen	2
Ursula Molter	2
Amos P. Kendall	2
Ruiwen Shu	2
Yujian Su	2
Herbert Stahl	1
Tamás Erdélyi	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Universally optimal distribution of points on spheres	2006	Henry Cohn Abhinav Kumar	32
+ PDF Chat	Asymptotics for discrete weighted minimal Riesz energy problems on rectifiable sets	2007	Sergiy Borodachov Douglas P. Hardin Edward B. Saff	27
+	Designs as maximum codes in polynomial metric spaces	1992	V.I. Levenshtein	23
+ PDF Chat	Asymptotics for minimal discrete energy on the sphere	1998	Arno B. J. Kuijlaars E. B. Saff	21
+	Minimal Riesz energy point configurations for rectifiable <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>d</mml:mi></mml:math>-dimensional manifolds	2004	Douglas P. Hardin Edward B. Saff	21
+	Spherical codes and designs	1977	P. Delsarte J.-M. Goethals J.J. Seidel	18
+ PDF Chat	Asymptotics for Minimal Discrete Riesz Energy on Curves in ℝ<i><sup>d</sup></i>	2004	Andrei Martı́nez-Finkelshtein V. Maymeskul Евгений Андреевич Рахманов Edward B. Saff	18
+ PDF Chat	Orthogonal Polynomials	1971		17
+ PDF Chat	Universal Lower Bounds for Potential Energy of Spherical Codes	2016	Peter Boyvalenkov Peter D Dragnev Douglas P. Hardin Edward B. Saff Maya Stoyanova	17
+	Geometric Measure Theory	1988	Herbert Fédérer	14
+	Fractal functions and interpolation	1986	Michael F. Barnsley	14
+	Quasi-uniformity of minimal weighted energy points on compact metric spaces	2011	Douglas P. Hardin Edward B. Saff J. Tyler Whitehouse	12
+ PDF Chat	A proof of the Kepler conjecture	2005	Thomas Hales	11
+	Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability	1995	Pertti Mattila	11
+	The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere	2012	J. Brauchart Douglas P. Hardin E. B. Saff	10
+	Upper bounds on the minimum distance of spherical codes	1996	Peter Boyvalenkov Danyo Danev S.P. Bumova	10
+ PDF Chat	Orthonormal bases of compactly supported wavelets	1988	Ingrid Daubechies	10
+	Minimal Riesz Energy Point Configurations for Rectifiable d-Dimensional Manifolds	2003	Douglas P. Hardin Edward B. Saff	9
+ PDF Chat	Asymptotics of best-packing on rectifiable sets	2007	Sergiy Borodachov Douglas P. Hardin Edward B. Saff	9
+	Iterated function systems and the global construction of fractals	1985	Michael F. Barnsley Stephen Demko	9
+ PDF Chat	Riesz polarization inequalities in higher dimensions	2013	Tamás Erdélyi Edward B. Saff	9
+	Geometry of Sets and Measures in Euclidean Spaces	1995	Pertti Mattila	9
+	Extremal dispositions of points on the sphere	1997	A. V. Kolushov V. A. Yudin А. В. Колущов В. А. Удин	9
+	Orthogonal Polynomials	1939	Gábor Szegő	9
+	Fractal Functions and Wavelet Expansions Based on Several Scaling Functions	1994	Jeffrey S. Geronimo Douglas P. Hardin Peter Massopust	9
+ PDF Chat	New upper bounds on sphere packings I	2003	Henry Cohn Noam D. Elkies	8
+ PDF Chat	Extremal arrangements of points and unit charges on a sphere: equilibrium configurations revisited	1977	Theodor W. Melnyk Osvald Knop William Robert Smith	8
+	On the distribution of Fekete points	1978	Björn E. J. Dahlberg	8
+ PDF Chat	Chebyshev constants for the unit circle	2012	Gergely Ambrus Keith Ball Tamás Erdélyi	7
+	Mathematical problems for the next century	1998	Steve Smale	7
+	Three-point bounds for energy minimization	2012	Henry Cohn Jeechul Woo	7
+	Analytic and Probabilistic Problems in Discrete Geometry	2009	Gergely Ambrus	7
+ PDF Chat	On the theory of potentials in locally compact spaces	1960	Bent Fuglede	7
+	Distributing many points on a sphere	1997	Edward B. Saff Arno B. J. Kuijlaars	7
+	On potentials in locally compact spaces	1961	Makoto Ohtsuka	7
+ PDF Chat	Renormalized Energy and Asymptotic Expansion of Optimal Logarithmic Energy on the Sphere	2016	Laurent Bétermin Étienne Sandier	7
+ PDF Chat	The kissing number in four dimensions	2008	Oleg R. Musin	7
+	Intertwining Multiresolution Analyses and the Construction of Piecewise-Polynomial Wavelets	1996	George C. Donovan Jeffrey S. Geronimo Douglas P. Hardin	7
+	None	2003	John J. Benedetto Matthew Fickus	7
+	Finite Packing and Covering	2004	Károly J. Böröczky	7
+ PDF Chat	Construction of Orthogonal Wavelets Using Fractal Interpolation Functions	1996	George C. Donovan Jeffrey S. Geronimo Douglas P. Hardin Peter Massopust	7
+	Multiresolution analyses based on fractal functions	1992	Douglas P. Hardin Bruce Kessler Peter Massopust	6
+ PDF Chat	Energy-Minimizing Error-Correcting Codes	2014	Henry Cohn Yufei Zhao	6
+	On maximal codes in polynomial metric spaces	1997	Peter Boyvalenkov Danyo Danev	6
+ PDF Chat	Extremal Systems of Points and Numerical Integration on the Sphere	2004	Ian H. Sloan Robert S. Womersley	6
+	Association schemes and coding theory	1998	P. Delsarte V.I. Levenshtein	6
+ PDF Chat	A Minimum Principle for Potentials with Application to Chebyshev Constants	2017	Alexander Reznikov Edward B. Saff Oleksandr Vlasiuk	6
+	Krawtchouk polynomials and universal bounds for codes and designs in Hamming spaces	1995	V.I. Levenshtein	6
+	Necessary Conditions for Existence of Some Designs in Polynomial Metric Spaces	1999	Peter Boyvalenkov Silvia Boumova Danyo Danev	6
+ PDF Chat	Minimal Discrete Energy on the Sphere	1994	Evguenii Andreevich Rakhmanov Edward B. Saff Yao Zhou	6