Quasi-conical domains with embedded eigenvalues

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F24%3A00587876" target="_blank" >RIV/61389005:_____/24:00587876 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/24:00377092
Result on the web
<a href="https://doi.org/10.1112/blms.13113" target="_blank" >https://doi.org/10.1112/blms.13113</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/blms.13113" target="_blank" >10.1112/blms.13113</a>

Result language
angličtina
Original language name
Quasi-conical domains with embedded eigenvalues
Original language description
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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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