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
Journal	Rendiconti di Matematica e delle Sue Applicazioni
Publication status	Published - 2022

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title = "Semiclassical bounds for spectra of biharmonic operators",

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.",

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AU - Provenzano, Luigi

AU - Stubbe, Joachim

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AB - 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.

UR - https://iris.uniupo.it/handle/11579/164982

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SN - 1120-7183

JO - Rendiconti di Matematica e delle Sue Applicazioni

JF - Rendiconti di Matematica e delle Sue Applicazioni

ER -

Semiclassical bounds for spectra of biharmonic operators

Abstract

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