On Persson's theorem in local Dirichlet spaces
type: Item
instance of: scholarly article
title: On Persson's theorem in local Dirichlet spaces
zbMATH Open document ID: 0908.31004
DOI: 10.4171/ZAA/825
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1999-03-10T00:00:00Z
review text: The author considers a strongly, local, regular and irreducible Dirichlet form \(\epsilon.\) He studies the analogue of the theorem of \textit{A. Persson} that is proved in [Math. Scand. 8, 143-153 (1960; Zbl 0145.14901)]to obtain a version, in his context, of his variational characterization of the bottom of the essential spectrum of elliptic differential operators in divergence form. Then, the author uses his result and those in cooperation with \textit{F. Cipriani} [J. Reine Angew. Math. 496, 163-179 (1998; Zbl 0891.35016)] to prove suitable coercitivity conditions and weighted \(L^p\) bounds for those eigenfunctions of the self-adjoint operator associated to \(\varepsilon\) whose eigenvalue lies below the essential spectrum of the ``small eigenfunctions''. To obtain this result the author uses a process contained in the book of \textit{S. A. Agmon} [Lectures on exponential decay of solutions of second-order elliptic equations, Princeton Univ. Press (1982; Zbl 0503.35001)].
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 47A11
Mathematics Subject Classification ID: 35P20
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 1182351
zbMATH Keywords: local Dirichlet spaces
zbMATH Keywords: Persson's theorem
zbMATH Keywords: small eigenfunctions
zbMATH Keywords: irreducible Dirichlet form
zbMATH Keywords: essential spectrum
zbMATH Keywords: elliptic differential operators in divergence form
zbMATH Keywords: bounds for eigenfunctions
author: Gabriele Grillo
reviewed by: Maria Alessandra Ragusa
MaRDI profile type: Publication
cites work: Q3969238
cites work: Asymptotic behaviour of relaxed Dirichlet problems involving a Dirichlet-Poincaré form
cites work: Pointwise properties of eigenfunctions and heat kernels of Dirichlet-Schrödinger operators
cites work: Q3764747
cites work: Bounds for the Discrete Part of the Spectrum of a Semi-Bounded Schrödinger Operator.
full work available at URL: https://doi.org/10.4171/zaa/825
OpenAlex ID: W2091049227
description: scientific article; zbMATH DE number 1182351