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

Dipartimento per lo Sviluppo Sostenibile e la Transizione Ecologica

Risultato della ricerca: Contributo su rivista › Articolo in rivista › 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.

Lingua originale	Inglese
Rivista	Rendiconti di Matematica e delle Sue Applicazioni
Stato di pubblicazione	Pubblicato - 2022

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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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N2 - 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.

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

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Semiclassical bounds for spectra of biharmonic operators

Abstract

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