Semiclassical bounds for spectra of biharmonic operators

Davide Buoso; Luigi Provenzano; Joachim Stubbe

Semiclassical bounds for spectra of biharmonic operators

Davide Buoso, Luigi Provenzano, Joachim Stubbe

Department of Sustainable Development and Ecological Transition

Research output: Contribution to journal › Article › peer-review

Abstract

We provide complementary semiclassical bounds for the Riesz means R1(z) of the eigenvalues of various biharmonic operators, with a second term in the expected power of z. The method we discuss makes use of the averaged variational principle (AVP), and yields two-sided bounds for individual eigenvalues, which are semiclassically sharp. The AVP also yields comparisons with Riesz means of different operators, in particular Laplacians.

Original language	English
Pages (from-to)	267-314
Number of pages	48
Journal	Rendiconti di Matematica e delle Sue Applicazioni
Volume	43
Issue number	4
Publication status	Published - 2022

Keywords

Biharmonic operator
Riesz means
averaged variational principle
eigenvalue asymptotics
semiclassical bounds for eigenvalues

Cite this

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KW - Riesz means

KW - averaged variational principle

KW - eigenvalue asymptotics

KW - semiclassical bounds for eigenvalues

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Semiclassical bounds for spectra of biharmonic operators

Abstract

Keywords

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