Ralph S. Phillips

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All published works

Action	Title	Year	Authors
+	Semi-Groups of Contraction Operators	2011	Ralph S. Phillips
+ PDF	Scattering theory for twisted automorphic functions	1998	Ralph S. Phillips
+	Dissolving a cusp form in the presence of multiplicities	1997	Chris Judge Ralph S. Phillips
+	Perturbation theory for twisted automorphic functions	1997	Ralph S. Phillips
+	None	1996	Ralph S. Phillips
+	Conjugacy Classes of Γ(2) and Spectral Rigidity	1995	Ralph S. Phillips
+ PDF	Conjugacy classes of Γ(2) and spectral rigidity	1995	Ralph S. Phillips
+	The Circle Problem in the Hyperbolic Plane	1994	Ralph S. Phillips Zeév Rudnick
+	Cusp forms for character varieties	1994	Ralph S. Phillips Peter Sarnak
+	Scattering theory for symmetric spaces of noncompact type	1993	Ralph S. Phillips Mehrdad Shahshahani
+	Automorphic spectrum and Fermi’s Golden Rule	1992	Ralph S. Phillips Peter Sarnak
+	Translation representation for automorphic solutions of the wave equation in non‐euclidean spaces, IV	1992	Peter D. Lax Ralph S. Phillips
+ PDF	Perturbation theory for the Laplacian on automorphic functions	1992	Ralph S. Phillips Peter Sarnak
+	The spectrum of fermat curves	1991	Ralph S. Phillips Peter Sarnak
+	Hodge theory on hyperbolic manifolds	1990	Rafe Mazzeo Ralph S. Phillips
+	Intertwining Operators and Residues	1989	Ralph S. Phillips
+	Extremals of determinants of Laplacians	1988	Brad Osgood Ralph S. Phillips Peter Sarnak
+	Compact isospectral sets of surfaces	1988	Brad Osgood Ralph S. Phillips Peter Sarnak
+	Ramanujan graphs	1988	Alexander Lubotzky Ralph S. Phillips Peter Sarnak
+	Scattering theory for the wave equation on a hyperbolic manifold	1987	Ralph S. Phillips Bettina Wiskott Alex Woo
+	Hecke operators and distributing points on <i>S</i><sup>2</sup>. II	1987	Alexander Lubotzky Ralph S. Phillips Peter Sarnak
+	Geodesics in homology classes	1987	Ralph S. Phillips Peter Sarnak
+	Scattering theory for the wave equation on a hyperbolic manifold	1987	Ralph S. Phillips Bettina Wiskott Alex Woo
+	Scattering Theory for the Wave Equation on a Hyperbolic Manifold	1987	Ralph S. Phillips
+	Hecke operators and distributing points on the sphere I	1986	Alexander Lubotzky Ralph S. Phillips Peter Sarnak
+	Explicit expanders and the Ramanujan conjectures	1986	Alexander Lubotzky Ralph S. Phillips Peter Sarnak
+	The weyl theorem and the deformation of discrete groups	1985	Ralph S. Phillips Peter Sarnak
+	On cusp forms for co-finite subgroups ofPSL(2,?)	1985	Ralph S. Phillips Peter Sarnak
+ PDF	Maass cusp forms	1985	Jean-Marc Deshouillérs Henryk Iwaniec Ralph S. Phillips Peter Sarnak
+ PDF	Translation Representations for Automorphic Solutions of The Wave Equation in Non-Euclidean Spaces; The Case of Finite Volume	1985	Peter D. Lax Ralph S. Phillips
+	On the spectrum of the Hecke groups	1985	Ralph S. Phillips Peter Sarnak
+	Translation representations for automorphic solutions of the wave equation in non‐euclidean spaces. III	1985	Peter D. Lax Ralph S. Phillips
+ PDF	Translation representations for automorphic solutions of the wave equation in non-Euclidean spaces; the case of finite volume	1985	Peter D. Lax Ralph S. Phillips
+ PDF	The laplacian for domains in hyperbolic space and limit sets of Kleinian groups	1985	Ralph S. Phillips Peter Sarnak
+	Translation representations for automorphic solutions of the wave equation in non‐euclidean spaces. II	1984	Peter D. Lax Ralph S. Phillips
+	Translation representations for automorphic solutions of the wave equation in non‐euclidean spaces. I	1984	Peter D. Lax Ralph S. Phillips
+	The Spectrum of the Laplacian for Domains in Hyperbolic Space and Limit Sets of Kleinian Groups	1984	Ralph S. Phillips
+	A local paley‐wiener theorem for the radon transform of <i>L</i><sub>2</sub> functions in a non‐euclidean setting	1982	Peter D. Lax Ralph S. Phillips
+	The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces	1982	Peter D. Lax Ralph S. Phillips
+	The Asymptotic Distribution of Lattice Points in Euclidean and Non-Euclidean Spaces	1982	Peter D. Lax Ralph S. Phillips
+	Translation representations for the solution of the non‐euclidean wave equation II	1981	Peter D. Lax Ralph S. Phillips
+	The Asymptotic Distribution of Lattice Points in Euclidean and Non-Euclidean Spaces	1981	Peter D. Lax Ralph S. Phillips
+ PDF	Scattering theory for automorphic functions	1980	Peter D. Lax Ralph S. Phillips
+	Translation representations for the solution of the non‐euclidean wave equation	1979	Peter D. Lax Ralph S. Phillips
+	An example of huygens' principle	1978	Peter D. Lax Ralph S. Phillips
+	Scattering theory for domains with non-smooth boundaries	1978	Peter D. Lax Ralph S. Phillips
+	§6. INCOMING AND OUTGOING SUBSPACES FOR THE AUTOMORPHIC WAVE EQUATION	1977	Peter D. Lax Ralph S. Phillips
+	§4. THE LAPLACE-BELTRAMI OPERATOR FOR THE MODULAR GROUP	1977	Peter D. Lax Ralph S. Phillips
+	§3. A MODIFIED THEORY FOR SECOND ORDER EQUATIONS WITH AN INDEFINITE ENERGY FORM	1977	Peter D. Lax Ralph S. Phillips
+	§5. THE AUTOMORPHIC WAVE EQUATIONS	1977	Peter D. Lax Ralph S. Phillips
+	§7. THE SCATTERING MATRIX FOR THE AUTOMORPHIC WAVE EQUATION	1977	Peter D. Lax Ralph S. Phillips
+	Scattering Theory for Automorphic Functions. (AM-87)	1977	Peter D. Lax Ralph S. Phillips
+	The scattering of sound waves by an obstacle	1977	Peter D. Lax Ralph S. Phillips
+	A scattering theory for automorphic functions	1974	Peter D. Lax Ralph S. Phillips
+	Scattering Theory for Dissipative Hyperbolic Systems	1974	Peter D. Lax Ralph S. Phillips
+	Scattering theory for dissipative hyperbolic systems	1973	Peter D. Lax Ralph S. Phillips
+	On the exterior problem for the reduced wave equation	1973	Ralph S. Phillips
+	The location of the poles of the scattering matrix	1972	Peter D. Lax Ralph S. Phillips
+	On the scattering frequencies of the laplace operator for exterior domains	1972	Peter D. Lax Ralph S. Phillips
+ PDF	Scattering Theory for the Acoustic Equation in an Even Number of Space Dimensions	1972	Peter D. Lax Ralph S. Phillips
+	Energy decay for the neutrino equation in the exterior of a torus	1971	Ralph S. Phillips Leonard Sarason
+	The paley‐wiener theorem for the radon transform	1970	Peter D. Lax Ralph S. Phillips
+	SCATTERING THEORY FOR HYPERBOLIC SYSTEMS	1970	Ralph S. Phillips
+ PDF	The eigenvalues of the Laplace operator for the exterior problem	1970	Peter D. Lax Ralph S. Phillips
+	Decaying modes for the wave equation in the exterior of an obstacle	1969	Peter D. Lax Ralph S. Phillips
+	Scattering Theory for Hyperbolic Equations	1969	Ralph S. Phillips
+	On the extension problem for dissipative operators	1968	Michael G. Crandall Ralph S. Phillips
+	Scattering Theory for Automorphic Functions. (AM-87), Volume 87	1967	Peter D. Lax Ralph S. Phillips
+	On Matrices Whose Real Linear Combinations are Nonsingular	1965	J. F. Adams Peter D. Lax Ralph S. Phillips
+ PDF	On matrices whose real linear combinations are non-singular	1965	J. F. Adams Peter D. Lax Ralph S. Phillips
+ PDF	Scattering theory	1964	Peter D. Lax Ralph S. Phillips
+ PDF	Exponential decay of solutions of the wave equation in the exterior of a star‐shaped obstacle	1963	Peter D. Lax Cathleen S. Morawetz Ralph S. Phillips
+ PDF	Semi-groups of positive contraction operators	1962	Ralph S. Phillips
+ PDF	The wave equation in exterior domains	1962	Peter D. Lax Ralph S. Phillips
+ PDF	The exponential decay of solutions of the wave equation in the exterior of a star-shaped obstacle	1962	Peter D. Lax Cathleen S. Morawetz Ralph S. Phillips
+ PDF	Dissipative operators in a Banach space	1961	G. Lumer Ralph S. Phillips
+ PDF	On the integration of the diffusion equation with boundary conditions.	1961	Ralph S. Phillips
+	Local boundary conditions for dissipative symmetric linear differential operators	1960	Peter D. Lax Ralph S. Phillips
+	Dissipative operators and parabolic partial differential equations	1959	Ralph S. Phillips
+ PDF	On a theorem due to Sz.-Nagy	1959	Ralph S. Phillips
+ PDF	Dissipative operators and hyperbolic systems of partial differential equations	1959	Ralph S. Phillips
+ PDF	Dissipative hyperbolic systems	1957	Ralph S. Phillips
+ PDF	Groups Of Positive Operators	1956	Heather A. Dye Ralph S. Phillips
+ PDF	The adjoint semi-group	1955	Ralph S. Phillips
+ PDF	Semi-groups of operators	1955	Ralph S. Phillips
+	An Inversion Formula for Laplace Transforms and Semi-Groups of Linear Operators	1954	Ralph S. Phillips
+ PDF	Perturbation Theory for Semi-Groups of Linear Operators	1953	Ralph S. Phillips
+ PDF	Perturbation theory for semi-groups of linear operators	1953	Ralph S. Phillips
+ PDF	Spectral Theory for Semi-Groups of Linear Operators	1951	Ralph S. Phillips
+ PDF	A note on ergodic theory	1951	Ralph S. Phillips
+ PDF	On one-parameter semi-groups of linear transformations	1951	Ralph S. Phillips
+ PDF	Spectral theory for semi-groups of linear operators	1951	Ralph S. Phillips
+	Bessel Function Approximations	1950	Ralph S. Phillips Henry Malin
+ PDF	On Fourier-Stieltjes integrals	1950	Ralph S. Phillips
+	On Weakly Compact Subsets of a Banach Space	1943	Ralph S. Phillips
+	Absolutely Convergent Fourier Expansions for Non-Commutative Normed Rings	1942	S. Bochner Ralph S. Phillips
+ PDF	On linear transformations	1940	Ralph S. Phillips
+ PDF	Integration in a convex linear topological space	1940	Ralph S. Phillips
+ PDF	A characterization of euclidean spaces	1940	Ralph S. Phillips

Common Coauthors

Coauthor	Papers Together
Peter D. Lax	39
Peter Sarnak	16
Alexander Lubotzky	4
Bettina Wiskott	2
Alex Woo	2
Brad Osgood	2
Cathleen S. Morawetz	2
Mehrdad Shahshahani	1
J. F. Adams	1
Michael G. Crandall	1
Zeév Rudnick	1
Rafe Mazzeo	1
Henry Malin	1
Jean-Marc Deshouillérs	1
S. Bochner	1
J. F. Adams	1
Henryk Iwaniec	1
Heather A. Dye	1
Chris Judge	1
G. Lumer	1
Leonard Sarason	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF	Functional Analysis and Semi-groups	1996	Einar Hille Robert A. Phillips	16
+ PDF	Scattering theory for automorphic functions	1980	Peter D. Lax Ralph S. Phillips	15
+	The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces	1982	Peter D. Lax Ralph S. Phillips	14
+	The Asymptotic Distribution of Lattice Points in Euclidean and Non-Euclidean Spaces	1982	Peter D. Lax Ralph S. Phillips	9
+	Translation representations for automorphic solutions of the wave equation in non‐euclidean spaces. I	1984	Peter D. Lax Ralph S. Phillips	8
+	On cusp forms for co-finite subgroups ofPSL(2,?)	1985	Ralph S. Phillips Peter Sarnak	7
+ PDF	Pseudo-laplaciens. I	1982	Yves Colin de Verdìère	7
+	Translation representations for the solution of the non‐euclidean wave equation	1979	Peter D. Lax Ralph S. Phillips	7
+	Théorie des opérations linéaires	1932	Stefan Banach	7
+	Harmonic Analysis and Discontinuous Groups in Weakly Symmetric Riemannian Spaces With Applications to Dirichlet Series	1956	Atle Selberg	7
+ PDF	The limit set of a Fuchsian group	1976	S. J. Patterson	7
+	�ber eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichlet scher Reihen durch Funktionalgleichungen	1949	Hans Maaß	6
+ PDF	Dissipative operators and hyperbolic systems of partial differential equations	1959	Ralph S. Phillips	6
+	Functional Analysis and Semi-Groups	1949	Richard G. Cooke	6
+	Spectral theory of automorphic functions	1982	Alexei B. Venkov	6
+	Symmetric positive linear differential equations	1958	K. O. Friedrichs	6
+	Scattering theory on real hyperbolic spaces and their compact perturbations	1980	Alex Woo	5
+	Elementary theory of Eisenstein series	1973	富雄久保田	5
+	Disappearance of Cusp Forms in Special Families	1994	Scott A. Wolpert	5
+	The spectrum of fermat curves	1991	Ralph S. Phillips Peter Sarnak	5
+	HARMONIC ANALYSIS ON RIEMANNIAN SYMMETRIC SPACES OF NEGATIVE CURVATURE AND SCATTERING THEORY	1976	M A Semenov-Tjan-Šanskiĭ	4
+	Die Resolvente zum Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. Teil I	1973	J�rgen Elstrodt	4
+	Local boundary conditions for dissipative symmetric linear differential operators	1960	Peter D. Lax Ralph S. Phillips	4
+ PDF	Lectures on Quasiconformal Mappings	2006	Lars V. Ahlfors	4
+ PDF	On one-parameter semi-groups of linear transformations	1951	Ralph S. Phillips	4
+	A local paley‐wiener theorem for the radon transform of <i>L</i><sub>2</sub> functions in a non‐euclidean setting	1982	Peter D. Lax Ralph S. Phillips	4
+ PDF	Maass cusp forms	1985	Jean-Marc Deshouillérs Henryk Iwaniec Ralph S. Phillips Peter Sarnak	4
+	Cusp forms for character varieties	1994	Ralph S. Phillips Peter Sarnak	4
+ PDF	The Selberg Trace Formula for PSL(2,ℝ)	1983	Dennis A. Hejhal	4
+	THE PARABOLIC DIFFERENTIAL EQUATIONS AND THE ASSOCIATED SEMI-GROUPS OF TRANSFORMATIONS	2015	William Feller	4
+	Translation representations for the solution of the non‐euclidean wave equation II	1981	Peter D. Lax Ralph S. Phillips	4
+	Scattering Theory for Automorphic Functions. (AM-87)	1977	Peter D. Lax Ralph S. Phillips	4
+	Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. II	1967	Walter Roelcke	3
+ PDF	Perturbation Theory for Linear Operators	1995	Tosio Kato	3
+	Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II	1961	Heinz Huber	3
+	The Surjectivity of Invariant Differential Operators on Symmetric Spaces I	1973	Sigurđur Helgason	3
+	A General Theory of Limits	1922	Eliakim Hastings Moore Hal L. Smith	3
+	The generalized huyghens' principle for reflecting bodies	1969	Cathleen S. Morawetz Donald Ludwig	3
+ PDF	Dissipative hyperbolic systems	1957	Ralph S. Phillips	3
+	The decay of solutions of the exterior initial‐boundary value problem for the wave equation	1961	Cathleen S. Morawetz	3
+	Meromorphic families of compact operators	1968	Stanly Steinberg	3
+ PDF	The wave equation in exterior domains	1962	Peter D. Lax Ralph S. Phillips	3
+	Decaying modes for the wave equation in the exterior of an obstacle	1969	Peter D. Lax Ralph S. Phillips	3
+	Asymptotic completeness for quantum mechanical potential scattering	1978	Volker Enß	3
+	Spektraldarstellung Linearer Transformationen des Hilbertschen Raumes	1942	Béla v. Sƶ. Nagy	3
+ PDF	On integration in vector spaces	1938	B. J. Pettis	3
+ PDF	Scattering Theory for the Acoustic Equation in an Even Number of Space Dimensions	1972	Peter D. Lax Ralph S. Phillips	3
+ PDF	The laplacian for domains in hyperbolic space and limit sets of Kleinian groups	1985	Ralph S. Phillips Peter Sarnak	3
+	Dissipative operators and parabolic partial differential equations	1959	Ralph S. Phillips	3
+ PDF	Uniformity in linear spaces	1938	Nelson Dunford	3