On the decomposition principle and a Persson type theorem for general\n regular Dirichlet forms

2017/05/29 by Daniel Lenz, Lenz, Daniel, Peter Stollmann +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1705.10398

openalex publication_date 2017/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a decomposition principle for general regular Dirichlet forms\nsatisfying a spatial local compactness condition. We use the decomposition\nprinciple to derive a Persson type theorem for the corresponding Dirichlet\nforms. In particular our setting covers Laplace-Beltrami operators on\nRiemannian manifolds, and Dirichlet forms associated to \α-stable\nprocesses in Euclidean space.\n

Citations

• On the parabolic kernel of the Schrödinger operator
• �ber gew�hnliche Differentialgleichungen mit Singularit�ten und die zugeh�rigen Entwicklungen willk�rlicher Funktionen

Related

• Decomposition formulae for Dirichlet forms and their corollaries
• On the Domains of Dirichlet Forms on Metric Measure Spaces
• Intrinsic metrics for non-local symmetric Dirichlet forms and\n applications to spectral theory
• Nonlinear Dirichlet forms, energy spaces, and calculus rules
• Geometric properties of Dirichlet forms under order isomorphisms