A real analyticity result for symmetric functions of the eigenvalues of a quasiperiodic spectral problem for the Dirichlet Laplacian

Autor:	J. Taskinen, Paolo Musolino, M. Lanza de Cristoforis
Rok vydání:	2021
Předmět:	Pure mathematics Algebra and Number Theory Laplace-Dirichlet problem Floquet-Bloch theory Real analytic domain perturbation periodic domain band-gap spectrum Symmetric function Settore MAT/05 - Analisi Matematica Dirichlet laplacian Quasiperiodic function Eigenvalues and eigenvectors Mathematics
Zdroj:	Journal of Operator Theory. 86:439-467
ISSN:	1841-7744 0379-4024
DOI:	10.7900/jot.2020jun08.2304
Popis:	As is well known, by the Floquet--Bloch theory for periodic problems, one can transform a spectral Laplace--Dirichlet problem in the plane with a set of periodic perforations into a family of ``model problems'' depending on a parameter η∈[0,2π]2 for quasiperiodic functions in the unit cell with a single perforation. We prove real analyticity results for the eigenvalues of the model problems upon perturbation of the shape of the perforation of the unit~cell.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2d905a4c8309bd4636b501d9df43009f https://doi.org/10.7900/jot.2020jun08.2304 Zobrazit plný text záznamu