Quasi-conical domains with embedded eigenvalues
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912217929089024 |
|---|---|
| author | Krejcirik, David Lotoreichik, Vladimir |
| author_facet | Krejcirik, David Lotoreichik, Vladimir |
| contents | The spectrum of the Dirichlet Laplacian on any quasi-conical open set coincides with the non-negative semi-axis. We show that there is a connected quasi-conical open set such that the respective Dirichlet Laplacian has a positive (embedded) eigenvalue. This open set is constructed as the tower of cubes of growing size connected by windows of vanishing size. Moreover, we show that the sizes of the windows in this construction can be chosen so that the absolutely continuous spectrum of the Dirichlet Laplacian is empty. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_08172 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quasi-conical domains with embedded eigenvalues Krejcirik, David Lotoreichik, Vladimir Spectral Theory Mathematical Physics Analysis of PDEs The spectrum of the Dirichlet Laplacian on any quasi-conical open set coincides with the non-negative semi-axis. We show that there is a connected quasi-conical open set such that the respective Dirichlet Laplacian has a positive (embedded) eigenvalue. This open set is constructed as the tower of cubes of growing size connected by windows of vanishing size. Moreover, we show that the sizes of the windows in this construction can be chosen so that the absolutely continuous spectrum of the Dirichlet Laplacian is empty. |
| title | Quasi-conical domains with embedded eigenvalues |
| topic | Spectral Theory Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2205.08172 |