On the decomposition principle and a Persson type theorem for general 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 #math.SP

paper · pdf · doi:10.48550/arxiv.1705.10398

19 pages, corrected references

openalex publication_date 2017/05/29 · arxiv created 2017/06/06 · arxiv updated 2017/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

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

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