Spectral triples, Coulhon-Varopoulos dimension and heat kernel estimates

DOI10.1016/j.aim.2024.109794MaRDI QIDQ6592207

Publication date: 24 August 2024

Published in: Advances in Mathematics (Search for Journal in Brave)

noncommutative geometry spectral dimension semigroups of operators spectral triples noncommutative \(\mathrm{L}^{p}\)-spaces Coulhon-Varopoulos dimension

Mathematics Subject Classification ID

Groups and semigroups of linear operators (47D03) Operator spaces and completely bounded maps (46L07) Noncommutative measure and integration (46L51) Noncommutative geometry (à la Connes) (58B34) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89)

Cites Work

Traceability of positive integral operators
Heat kernel bounds on metric measure spaces and some applications
Noncommutative potential theory: a survey
Harmonic analysis on quantum tori
Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
Heat trace and spectral action on the standard Podleś sphere
Smooth Fourier multipliers on group von Neumann algebras
On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
Neuer Beweis und Verallgemeinerung einiger Tauberian-Sätze.
Dirichlet forms and symmetric Markov processes.
Heat kernel asymptotics for the measurable Riemannian structure on the Sierpinski gasket
Gaussian upper bounds for the heat kernel on arbitrary Riemannian manifolds
Traceable integral kernels on countably generated measure spaces
Heat trace asymptotics on equiregular sub-Riemannian manifolds
Dirichlet forms of fractals and products of random matrices
Localization and tensorization properties of the curvature-dimension condition for metric measure spaces
Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
Hardy-Littlewood theory for semigroups
On the parabolic kernel of the Schrödinger operator
Upper bounds for symmetric Markov transition functions
Brownian motion on the Sierpinski gasket
Dirichlet forms and analysis on Wiener space
Introduction to the theory of (non-symmetric) Dirichlet forms
Non-commutative symmetric Markov semigroups
Primitive ideals in enveloping algebras
Potential theory on the infinite dimensional torus
An example of a non nuclear C*-algebra, which has the metric approximation property
What is not in the domain of the Laplacian on Sierpinski gasket type fractals
Schrödinger semigroups on manifolds
Dirichlet forms and Markovian semigroups on standard forms of von Neumann algebras
Derivations as square roots of Dirichlet forms
Sur une courbe dont tout point est un point de ramification.
Lectures on analysis on metric spaces
Amenability and subexponential spectral growth rate of Dirichlet forms on von Neumann algebras
Short-time behavior of the heat kernel and Weyl's law on \(\mathrm{RCD}^*(K,N)\) spaces
Tosio Kato's work on non-relativistic quantum mechanics. I
Kernel operators in \(L^ p\)-spaces associated with semifinite von Neumann algebras
Theory of operator algebras. II
Lipschitz algebras and derivations of von Neumann algebras
Complete logarithmic Sobolev inequalities via Ricci curvature bounded below
Riesz transforms, Hodge-Dirac operators and functional calculus for multipliers
On the Sobolev embedding properties for compact matrix quantum groups of Kac type
Fisher information and logarithmic Sobolev inequality for matrix-valued functions
Monotonicity and rigidity of the \(\mathcal{W}\)-entropy on \(\mathsf{RCD} (0, N)\) spaces
The globalization theorem for the curvature-dimension condition
Noncommutative geometry and particle physics
Spectral triples for the Sierpinski gasket
Metric and spectral triples for Dirichlet and resistance forms
Ricci curvature for metric-measure spaces via optimal transport
Ultracontractivity and eigenvalues: Weyl's law for the Dirichlet-to-Neumann operator
Radial processes on \(\mathsf{RCD}^\ast(K,N)\) spaces
Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
Metric measure spaces with Riemannian Ricci curvature bounded from below
Measurable Riemannian geometry on the Sierpinski gasket: the Kusuoka measure and the Gaussian heat kernel estimate
Kernel estimates for a class of Schrödinger semigroups
The functional calculus for sectorial operators
On the geometry of metric measure spaces. I
On the geometry of metric measure spaces. II
A short course on operator semigroups
Operator algebras. Theory of \(C^*\)-algebras and von Neumann algebras
Embedding of \(\mathrm{RCD}^\ast (K,N)\) spaces in \(L^2\) via eigenfunctions
Singular traces. Volume 2. Trace formulas
Analysis on fractals
Stochastic analysis on manifolds
Partial Differential Equations for Probabilists
The Gauss-Bonnet Theorem for the noncommutative two torus
On the differential structure of metric measure spaces and applications
Analysis and Geometry of the Measurable Riemannian Structure on the Sierpiński Gasket
Vector Analysis on Fractals and Applications
On operator norms for hyperbolic groups
Approximation properties for locally compact quantum groups
Schrödinger semigroups
Noncommutative harmonic analysis on semigroup and ultracontractivity
Fourier and Fourier-Stieltjes Algebras on Locally Compact Groups
Modular curvature for noncommutative two-tori
Continuity of Solutions of Parabolic and Elliptic Equations
Curvature in noncommutative geometry
Modular Gaussian curvature
Manifolds with Ricci Curvature in the Kato Class: Heat Kernel Bounds and Applications
Mixed-norm inequalities and operator space 𝐿_{𝑝} embedding theory
Rapidly Decreasing Functions in Reduced C ∗ -Algebras of Groups
A reduction method for noncommutative 𝐿_{𝑝}-spaces and applications
Noncommutative Riesz transforms — a probabilistic approach
Two-sided estimates of fundamental solutions of second-order parabolic equations, and some applications
Explicit Constants for Gaussian Upper Bounds on Heat Kernels
One-Parameter Semigroups for Linear Evolution Equations
Integral representations of resolvents and semigroups
Harmonic Analysis and Ultracontractivity
L ^p Spectral Theory of Higher-Order Elliptic Differential Operators
Spectral Action in Noncommutative Geometry
Smooth Fourier multipliers in group algebras via Sobolev dimension
Introduction to the Rapid Decay property
Interpolation Theory
ON APPROXIMATION PROPERTIES FOR OPERATOR SPACES
Analysis and Geometry of Markov Diffusion Operators
Tosio Kato’s work on non-relativistic quantum mechanics, Part 2
New stability results for sequences of metric measure spaces with uniform Ricci bounds from below
Energy measures for diffusions on fractals: a survey
Gibbs Semigroups
Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces
Noncommutative harmonic analysis on semigroups
Dirichlet Forms on Noncommutative Spaces
Semigroups of Linear Operators
Compact metric spaces, Fredholm modules, and hyperfiniteness
Relative entropy for von Neumann subalgebras
Theory of operator algebras I.
Sharp Gaussian upper bounds for Schrödinger heat kernel on gradient shrinking Ricci solitons
Sobolev algebras on Lie groups and noncommutative geometry
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