Functional inequalities for empty essential spectrum

DOI10.1006/jfan.1999.3516zbMath0946.58010OpenAlexW2057010857MaRDI QIDQ1969496

Feng-Yu Wang

Publication date: 8 October 2000

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1999.3516

zbMATH Keywords

essential spectrumsuper-Poincaré inequality

Mathematics Subject Classification ID

Analysis on supermanifolds or graded manifolds (58C50) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items

Criteria for super- and weak-Poincaré inequalities of ergodic birth-death processes ⋮ Hypercontractivity for Markov semi-groups ⋮ Estimate the exponential convergence rate of \(f\)-ergodicity via spectral gap ⋮ Gradient estimates of Dirichlet heat semigroups and application to isoperimetric inequalities. ⋮ Intrinsic ultracontractivity of Feynman-Kac semigroups for symmetric jump processes ⋮ Estimates for invariant probability measures of degenerate SPDEs with singular and path-dependent drifts ⋮ Functional inequalities for convolution probability measures ⋮ Trends to equilibrium in total variation distance ⋮ Compactness of Schrödinger semigroups with unbounded below potentials ⋮ A Harnack-type inequality for non-symmetric Markov semigroups ⋮ On supercontractivity for Markov semigroups ⋮ Weak logarithmic Sobolev inequalities and entropic convergence ⋮ Perturbations of functional inequalities using growth conditions ⋮ Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry ⋮ Nash inequality for diffusion processes associated with Dirichlet distributions ⋮ Improved intermediate asymptotics for the heat equation ⋮ Diffusion and kinetic transport with very weak confinement ⋮ Higher order eigenvalues for non-local Schrödinger operators ⋮ Functional inequalities and subordination: Stability of Nash and Poincaré inequalities ⋮ Lift zonoid order and functional inequalities ⋮ Functional inequalities for weighted gamma distribution on the space of finite measures ⋮ Spectral inequalities for operators on \(H\)-type groups ⋮ Higher order coercive inequalities ⋮ From concentration to logarithmic Sobolev and Poincaré inequalities ⋮ Isoperimetry and stability of hyperplanes for product probability measures ⋮ Super Poincaré inequalities, Orlicz norms and essential spectrum ⋮ Functional inequalities for nonlocal Dirichlet forms with finite range jumps or large jumps ⋮ On improvement of summability properties in nonautonomous Kolmogorov equations ⋮ Poincaré inequalities and dimension free concentration of measure ⋮ Non ultracontractive heat kernel bounds by Lyapunov conditions ⋮ Exponential convergence rate in entropy ⋮ Harnack and super poincaré inequalities for generalized Cox-Ingersoll-Ross model ⋮ Functional inequalities for stable-like Dirichlet forms ⋮ From super Poincaré to weighted log-Sobolev and entropy-cost inequalities ⋮ Mass transport and variants of the logarithmic Sobolev inequality ⋮ Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincaré ⋮ Uniform gradient estimates on manifolds with a boundary and applications ⋮ Poincar\'e Inequality for Dirichlet Distributions and Infinite-Dimensional Generalizations ⋮ ON THE COMPACTNESS OF MANIFOLDS ⋮ Isoperimetric inequalities for non-local Dirichlet forms ⋮ Functional inequalities on arbitrary Riemannian manifolds ⋮ deviation bounds for additive functionals of markov processes ⋮ Spectral density and Sobolev inequalities for pure and mixed states ⋮ \(L^p\)-Poincaré inequality for general symmetric forms ⋮ Intrinsic ultracontractivity on Riemannian manifolds with infinite volume measures ⋮ On the equivalence between \(p\)-Poincaré inequalities and \(L^r\)-\(L^q\) regularization and decay estimates of certain nonlinear evolutions ⋮ A generalization of Poincaré and log-Sobolev inequalities ⋮ New estimates for the bottom of the spectrum of Schrödinger operators ⋮ Weak Poincaré inequalities and \(L^2\)-convergence rates of Markov semigroups ⋮ Capacitary criteria for Poincaré-type inequalities ⋮ Functional inequalities for particle systems on Polish spaces ⋮ Dimension-free Harnack inequality and its applications ⋮ Schröodinger equations and heat kernel upper bounds on metric spaces ⋮ On the empty essential spectrum for Markov processes in dimension one ⋮ Sharp estimates for intrinsic ultracontractivity on \(C^{1,\alpha}\)-domains ⋮ FUNCTIONAL INEQUALITIES, SEMIGROUP PROPERTIES AND SPECTRUM ESTIMATES ⋮ Harnack inequality and applications for infinite-dimensional GEM processes ⋮ Functional inequality on path space over a non-compact Riemannian manifold ⋮ Ergodicity for time-changed symmetric stable processes ⋮ Multiple sets exponential concentration and higher order eigenvalues ⋮ Lyapunov conditions for super Poincaré inequalities ⋮ Super-Poincaré and Nash-type inequalities for subordinated semigroups ⋮ Essential spectrum and Weyl asymptotics for discrete Laplacians ⋮ Exponential convergence in Lp-Wasserstein distance for diffusion processes without uniformly dissipative drift ⋮ On \(F\)-Sobolev and Orlicz-Sobolev inequalities ⋮ Compactness and density estimates for weighted fractional heat semigroups ⋮ Super and weak Poincaré inequalities for hypoelliptic operators ⋮ The spectral bound and principal eigenvalues of Schrödinger operators on Riemannian manifolds ⋮ Sobolev-Orlicz imbeddings, weak compactness, and spectrum ⋮ Weak Poincaré inequalities, decay of Markov semigroups and concentration of measures ⋮ Functional inequalities and spectrum estimates: The infinite measure case ⋮ Intrinsic contractivity properties of Feynman-Kac semigroups for symmetric jump processes with infinite range jumps

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Pure point spectrum and negative curvature for noncompact manifolds
• On the spectrum of non-compact manifolds with finite volume
• Some boundedness properties of certain stationary diffusion semigroups
• Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
• On the parabolic kernel of the Schrödinger operator
• Upper bounds for symmetric Markov transition functions
• A relation between growth and the spectrum of the Laplacian
• Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
• Uniform positivity improving property, Sobolev inequalities, and spectral gaps
• Herbst inequalities for supercontractive semigroups
• Logarithmic Sobolev inequalities and exponential integrability
• On estimation of the logarithmic Sobolev constant and gradient estimates of heat semigroups
• Logarithmic Sobolev inequalities on noncompact Riemannian manifolds
• On the essential spectrum of the Laplacian on complete manifolds
• On Persson's theorem in local Dirichlet spaces
• Existence of the spectral gap for elliptic operators
• Ultracontractivity and Nash type inequalities
• Moment estimates derived from Poincaré and logarithmic Sobolev inequalities
• $C^\infty$ approximations of convex, subharmonic, and plurisubharmonic functions
• Comparison Theorems on Dirichlet Norms and their Applications
• Exhaustion functions and the spectrum of Riemannian manifolds
• Some isoperimetric inequalities and eigenvalue estimates
• Isoperimetric constants and the first eigenvalue of a compact riemannian manifold
• A Simple Analytic Proof of an Inequality by P. Buser
• Logarithmic Sobolev inequalities and the growth of 𝐿^{𝑝} norms
• Sobolev inequalities in disguise
• Cheeger's inequalities for general symmetric forms and existence criteria for spectral gap