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 twosided bounds for individual eigenvalues, which are semiclassically sharp. The AVP also yields comparisons with Riesz means of different operators, in particular Laplacians.
Semiclassical bounds for spectra of biharmonic operators / Buoso, Davide; Provenzano, Luigi; Stubbe, Joachim. - In: RENDICONTI DI MATEMATICA E DELLE SUE APPLICAZIONI. - ISSN 2532-3350. - (2022).
Semiclassical bounds for spectra of biharmonic operators
Luigi Provenzano
;
2022
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 twosided bounds for individual eigenvalues, which are semiclassically sharp. The AVP also yields comparisons with Riesz means of different operators, in particular Laplacians.File allegati a questo prodotto
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