Generalized Solutions and Spectrum for Dirichlet Forms on Graphs
From MaRDI portal
Publication:5198980
DOI10.1007/978-3-0346-0244-0_10zbMath1227.47023arXiv1002.1040OpenAlexW1610017708MaRDI QIDQ5198980
Matthias Keller, Sebastian Haeseler
Publication date: 10 August 2011
Published in: Random Walks, Boundaries and Spectra (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1002.1040
Related Items (31)
A Feynman-Kac-Itô formula for magnetic Schrödinger operators on graphs ⋮ The generalized porous medium equation on graphs: existence and uniqueness of solutions with \(\ell^1\) data ⋮ Generalized eigenfunctions and eigenvalues: a unifying framework for Shnol-type theorems ⋮ Volume growth, spectrum and stochastic completeness of infinite graphs ⋮ Sharp Davies-Gaffney-Grigor'yan lemma on graphs ⋮ Stochastic completeness of graphs: bounded Laplacians, intrinsic metrics, volume growth and curvature ⋮ Global properties of Dirichlet forms in terms of Green's formula ⋮ Overview of the topical collection: harmonic analysis on combinatorial graphs ⋮ Optimal Hardy inequalities for Schrödinger operators on graphs ⋮ Schnol's theorem and spectral properties of massless Dirac operators with scalar potentials ⋮ Boundary representation of Dirichlet forms on discrete spaces ⋮ Lower bound to the entanglement entropy of the XXZ spin ring ⋮ Optimal Hardy weights on the Euclidean lattice ⋮ A non-local quasi-linear ground state representation and criticality theory ⋮ Essential self-adjointness for combinatorial Schrödinger operators. II. Metrically non complete graphs ⋮ A note on self-adjoint extensions of the Laplacian on weighted graphs ⋮ Global properties of Dirichlet forms on discrete spaces ⋮ Spectral analysis of the Laplacian acting on discrete cusps and funnels ⋮ Diffusion determines the recurrent graph ⋮ Existence of nonnegative solutions for parabolic problem on Dirichlet forms ⋮ Maximal accretive extensions of Schrödinger operators on vector bundles over infinite graphs ⋮ Riesz decompositions for Schrödinger operators on graphs ⋮ Hardy inequality and asymptotic eigenvalue distribution for discrete Laplacians ⋮ Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory ⋮ A gradient estimate for positive functions on graphs ⋮ Martin boundary of Brownian motion on Gromov hyperbolic metric graphs ⋮ Intrinsic Metrics on Graphs: A Survey ⋮ Essential spectrum and Weyl asymptotics for discrete Laplacians ⋮ Eigenfunctions growth of \(\mathcal{R}\)-limits on graphs ⋮ (Weak) Hardy and Poincaré inequalities and criticality theory ⋮ Spectral and scattering theory for topological crystals perturbed by infinitely many new edges
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Eigenvalue bounds for perturbations of Schrödinger operators and Jacobi matrices with regular ground states
- Nonlinear ground state representations and sharp Hardy inequalities
- Spectrum and continuum eigenfunctions of Schrödinger operators
- Ergodic properties of nonnegative matrices. II
- Positive solutions of elliptic equations
- Dirichlet forms and symmetric Markov processes
- Heat kernel estimates and parabolic Harnack inequalities on graphs and resistance forms
- Related aspects of positivity in Riemannian geometry
- On the equivalence of two types of oscillation for elliptic operators
- Nonoscillatory elliptic equations
- The Allegretto-Piepenbrink theorem for strongly local Dirichlet forms
- Ergodic properties of nonnegative matrices. I
- Sch'nol's theorem for strongly local forms
- Dirichlet forms and stochastic completeness of graphs and subgraphs
- Generalized Eigenfunctions and Spectral Theory for Strongly Local Dirichlet Forms
- Unbounded Laplacians on Graphs: Basic Spectral Properties and the Heat Equation
- A Survey on Spectra of infinite Graphs
- The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
- Differential equations on riemannian manifolds and their geometric applications
- Difference Equations, Isoperimetric Inequality and Transience of Certain Random Walks
- Random Walks on Infinite Graphs and Groups
- Heat kernel and essential spectrum of infinite graphs
- Quantum graphs: II. Some spectral properties of quantum and combinatorial graphs
- Eigenvalues of Non-Negative Matrices
- Caught by disorder. Bound states in random media
This page was built for publication: Generalized Solutions and Spectrum for Dirichlet Forms on Graphs