Sharp spectral bounds for complex perturbations of the indefinite Laplacian

Autor:	Cuenin, Jean-Claude, Ibrogimov, Orif O.
Rok vydání:	2020
Předmět:	Mathematics - Spectral Theory Mathematical Physics
Druh dokumentu:	Working Paper
Popis:	We derive quantitative bounds for eigenvalues of complex perturbations of the indefinite Laplacian on the real line. Our results substantially improve existing results even for real-valued potentials. For $L^1$-potentials, we obtain optimal spectral enclosures which accommodate also embedded eigenvalues, while our result for $L^p$-potentials yield sharp spectral bounds on the imaginary parts of eigenvalues of the perturbed operator for all $p\in[1,\infty)$. The sharpness of the results are demonstrated by means of explicit examples. Comment: References added before Theorem 2 and 4
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2004.10471 Zobrazit plný text záznamu View this record from Arxiv