Operators with singular continuous spectrum, VI. Graph Laplacians and Laplace-Beltrami operators

Barry Simon

Type: Article

Publication Date: 1996-01-01

Citations: 33

DOI: https://doi.org/10.1090/s0002-9939-96-03245-5

View Publication

Download PDF

Abstract

Examples are constructed of Laplace-Beltrami operators and graph Laplacians with singular continuous spectrum.

Locations

Proceedings of the American Mathematical Society - View - PDF
CaltechAUTHORS (California Institute of Technology) - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Absence of singular continuous spectrum for some geometric Laplacians	2013	Leonardo A. Cano García
+	Jacobi Operators with Singular Continuous Spectrum	2005	Deborah Koslover
+	Spectral properties for discrete and continuous Laplacians	2006	Jin Feng Thomas G. Kurtz
+	Eigenvalues of Laplacians and other geometric operators	2004	Alexander Grigor’yan Shing Tung Yau
+ PDF Chat	Functions of the Laplace-Beltrami operator	1996	Yu. Safarov
+ PDF Chat	Spectra of the Discrete and Continuous Laplacians on Graphs and Riemannian Manifolds.	1997	Hajime Urakawa
+	Spectral Properties of the Laplace-Beltrami Operator and Applications	2001	Mircea Craioveanu Mircea Puta Themistocles M. Rassias
+	EIGENFUNCTIONS OF THE LAPLACE OPERATOR AND METHOD OF GRAPHS	1965	N. Ya. Vilenkin G. I. Kuznetsov Ya.A. Smorodinskii
+	Laplace-Beltrami operator	1977	Leo Sario Mitsuru Nakai Cecilia Wang Lung Ock Chung
+	The spectrum of the -Laplacian with singular weight	2012	Marcelo Montenegro Sebastián Lorca
+ PDF Chat	Infinity Laplacian equations with singular absorptions	2022	Damião J. Araújo Ginaldo S. Sá
+	8 Fractional Laplacian type operators	2021	Ireneo Peral Alonso Fernando Soria
+	Discrete Laplacian in a half-space with a periodic surface potential : an overview on analytical investigations (Spectral and Scattering Theory and Related Topics)	2021	Serge Richard
+	Spectral Analysis of the Laplacian with a Discontinuous Coefficient	2009	Calvin H. Wilcox
+	Spectra and eigenfunctions of laplacians	1997	Peter Sarnak
+	Eigenfunctions and eigenvalues of Laplacian	1975	Shiu Yuen Cheng
+	Some Classes of Dirac Operators with Singular Potentials	2004	Rauf Amirov И. М. Гусейнов
+	$p$-Laplace operator on a connected finite graph	2023	Lin Feng Wang
+	Laplacians on infinite graphs: discrete vs continuous	2021	Aleksey Kostenko Noema Nicolussi
+	The Laplace operator on graphs	2018	Alexander Grigorâyan

Works That Cite This (34)

Action	Title	Year	Authors
+	Noncompact complete Riemannian manifolds with singular continuous spectrum embedded into the essential spectrum of the Laplacian, I. The hyperbolic case	2020	Svetlana Jitomirskaya Wencai Liu
+ PDF Chat	Singular continuous and dense point spectrum for sparse trees with finite dimensions	2007	Jonathan Breuer
+ PDF Chat	Tosio Kato’s work on non-relativistic quantum mechanics: part 1	2018	Barry Simon
+ PDF Chat	Singular Continuous Spectrum for the Laplacian on Certain Sparse Trees	2006	Jonathan Breuer
+	Path Laplacian operators and superdiffusive processes on graphs. I. One-dimensional case	2017	Ernesto Estrada Ehsan M. Hameed Naomichi Hatano Matthias Langer
+ PDF Chat	Zero Measure and Singular Continuous Spectra for Quantum Graphs	2020	David Damanik Licheng Fang Selim Sukhtaiev
+	Spectral analysis for convolution operators on locally compact groups	2007	Marius Măntoiu Rafael Tiedra de Aldecoa
+ PDF Chat	Spectral Analysis for Adjacency Operators on Graphs	2007	Marius Măntoiu Serge Richard Rafael Tiedra de Aldecoa
+ PDF Chat	The Canopy Graph and Level Statistics for Random Operators on Trees	2006	Michael Aizenman Simone Warzel
+	Spectral analysis for convolution operators on locally compact groups	2007	Marius Măntoiu Rafael Tiedra de Aldecoa

Works Cited by This (9)

Action	Title	Year	Authors
+ PDF Chat	$L\sp p$ norms of the Borel transform and the decomposition of measures	1995	Barry Simon
+ PDF Chat	Operators with singular continuous spectrum, V. Sparse potentials	1996	Barry Simon Günter Stolz
+ PDF Chat	Anderson localization for Bernoulli and other singular potentials	1987	René Carmona Abel Klein Fabio Martinelli
+ PDF Chat	Operators with Singular Continuous Spectrum: I. General Operators	1995	Barry Simon
+ PDF Chat	Operators with singular continuous spectrum: III. Almost periodic Schrödinger operators	1994	Svetlana Jitomirskaya Barry Simon
+ PDF Chat	Operators with singular continuous spectrum, IV. Hausdorff dimensions, rank one perturbations, and localization	1996	Rafael del Río Svetlana Jitomirskaya Yoram Last Barry Simon
+ PDF Chat	Operators with singular continuous spectrum: II. Rank one operators	1994	Rafael del Río Nikolai Makarov Barry Simon
+	Eigenvalue asymptotics of the Neumann Laplacian of regions and manifolds with cusps	1992	Vojkan Jakšić S. A. Molčanov Barry Simon
+ PDF Chat	L p Norms of the Borel Transform and the Decomposition of Measures	1995	Barry Simon