Functional inequalities for empty essential spectrum
type: Item
instance of: scholarly article
title: Functional inequalities for empty essential spectrum
zbMATH Open document ID: 0946.58010
author: Feng-Yu Wang
published in: Journal of Functional Analysis
publication date: 2000-10-08T00:00:00Z
review text: The author proves the equivalence between the super-Poincaré inequality and the empty essential spectrum. Also some connections with the \(F\)-Sobolev inequality and the Nash inequality are nicely pointed out.
Mathematics Subject Classification ID: 58C50
Mathematics Subject Classification ID: 58C40
zbMATH DE Number: 1416446
zbMATH Keywords: super-Poincaré inequality
zbMATH Keywords: essential spectrum
reviewed by: Mircea Puta
MaRDI profile type: Publication
full work available at URL: jfan.1999.3516
OpenAlex ID: W2057010857
cites work: Uniform positivity improving property, Sobolev inequalities, and spectral gaps
cites work: Logarithmic Sobolev inequalities and exponential integrability
cites work: Moment estimates derived from Poincaré and logarithmic Sobolev inequalities
cites work: Sobolev inequalities in disguise
cites work: A relation between growth and the spectrum of the Laplacian
cites work: On the spectrum of non-compact manifolds with finite volume
cites work: Upper bounds for symmetric Markov transition functions
cites work: Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
cites work: Q4003728
cites work: Cheeger's inequalities for general symmetric forms and existence criteria for spectral gap
cites work: Ultracontractivity and Nash type inequalities
cites work: Some isoperimetric inequalities and eigenvalue estimates
cites work: Q4041031
cites work: Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
cites work: Exhaustion functions and the spectrum of Riemannian manifolds
cites work: Pure point spectrum and negative curvature for noncompact manifolds
cites work: $C^\infty$ approximations of convex, subharmonic, and plurisubharmonic functions
cites work: On Persson's theorem in local Dirichlet spaces
cites work: Herbst inequalities for supercontractive semigroups
cites work: On the essential spectrum of the Laplacian on complete manifolds
cites work: Some boundedness properties of certain stationary diffusion semigroups
cites work: A Simple Analytic Proof of an Inequality by P. Buser
cites work: Q4938929
cites work: On the parabolic kernel of the Schrödinger operator
cites work: Q3909512
cites work: Logarithmic Sobolev inequalities and the growth of 𝐿^{𝑝} norms
cites work: Comparison Theorems on Dirichlet Norms and their Applications
cites work: On estimation of the logarithmic Sobolev constant and gradient estimates of heat semigroups
cites work: Logarithmic Sobolev inequalities on noncompact Riemannian manifolds
cites work: Existence of the spectral gap for elliptic operators
cites work: Q4533167
cites work: Isoperimetric constants and the first eigenvalue of a compact riemannian manifold
DOI: 10.1006/JFAN.1999.3516
description: scientific article; zbMATH DE number 1416446