A real analyticity result for symmetric functions of the eigenvalues of a quasiperiodic spectral problem for the Dirichlet Laplacian
Dipartimento di Matematica ``Tullio Levi-Civita'', Universita degli Studi di Padova, Padova, 35121, Italy, Massimo Lanza de Cristoforis, Паоло Мусоліно, Dipartimento di Scienze Molecolari e Nanosistemi, Universita Ca' Foscari Venezia, Venezia Mestre, 30170, Italy, Jari Taskinen · Journal of Operator Theory · 2021
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.