Semiclassical bounds for spectra of biharmonic operators
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 eigenvalu...
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
2022-06-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
| Subjects: | |
| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2022(4)/267-314.pdf |
| _version_ | 1797821787949498368 |
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| author | Davide Buoso Luigi Provenzano Joachim Stubbe |
| author_facet | Davide Buoso Luigi Provenzano Joachim Stubbe |
| author_sort | Davide Buoso |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-13T09:57:58Z |
| format | Article |
| id | doaj.art-bd5731d272dd4b118b509b86a31fc0dd |
| institution | Directory Open Access Journal |
| issn | 1120-7183 2532-3350 |
| language | English |
| last_indexed | 2024-03-13T09:57:58Z |
| publishDate | 2022-06-01 |
| publisher | Sapienza Università Editrice |
| record_format | Article |
| series | Rendiconti di Matematica e delle Sue Applicazioni |
| spelling | doaj.art-bd5731d272dd4b118b509b86a31fc0dd2023-05-23T13:03:02ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33502022-06-01433-4267314Semiclassical bounds for spectra of biharmonic operatorsDavide Buoso0Luigi Provenzano1Joachim Stubbe2Dipartimento per lo Sviluppo Sostenibile e la Transizione Ecologica (DiSSTE), Universit degli Studi del Piemonte Orientale “A. Avogadro”, Complesso S. Giuseppe - piazza Sant’ Eusebio 5, 13100 Vercelli (Italy)Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Universit`a di Roma, Via Antonio Scarpa 16, 00161 Roma (Italy)EPFL, SB MATH SCI-SB-JS, Station 8, CH-1015 Lausanne (Switzerland)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.https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2022(4)/267-314.pdfbiharmonic operatorriesz meanseigenvalue asymptoticssemiclassical bounds for eigenvaluesaveraged variational principle |
| spellingShingle | Davide Buoso Luigi Provenzano Joachim Stubbe Semiclassical bounds for spectra of biharmonic operators Rendiconti di Matematica e delle Sue Applicazioni biharmonic operator riesz means eigenvalue asymptotics semiclassical bounds for eigenvalues averaged variational principle |
| title | Semiclassical bounds for spectra of biharmonic operators |
| title_full | Semiclassical bounds for spectra of biharmonic operators |
| title_fullStr | Semiclassical bounds for spectra of biharmonic operators |
| title_full_unstemmed | Semiclassical bounds for spectra of biharmonic operators |
| title_short | Semiclassical bounds for spectra of biharmonic operators |
| title_sort | semiclassical bounds for spectra of biharmonic operators |
| topic | biharmonic operator riesz means eigenvalue asymptotics semiclassical bounds for eigenvalues averaged variational principle |
| url | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/2022(4)/267-314.pdf |
| work_keys_str_mv | AT davidebuoso semiclassicalboundsforspectraofbiharmonicoperators AT luigiprovenzano semiclassicalboundsforspectraofbiharmonicoperators AT joachimstubbe semiclassicalboundsforspectraofbiharmonicoperators |