Global Perturbation of Nonlinear Eigenvalues
| Autor: | Juan Carlos Sampedro, Julián López-Gómez |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
General Mathematics
010102 general mathematics Zero (complex analysis) Statistical and Nonlinear Physics Surface (topology) 01 natural sciences 010101 applied mathematics Section (category theory) Operator (computer programming) Cover (topology) 0101 mathematics Perturbation theory Eigenvalues and eigenvectors Eigenvalue perturbation Mathematics Mathematical physics |
| Zdroj: | Advanced Nonlinear Studies. 21:229-249 |
| ISSN: | 2169-0375 1536-1365 2021-2127 |
| DOI: | 10.1515/ans-2021-2127 |
| Popis: | This paper generalizes the classical theory of perturbation of eigenvalues up to cover the most general setting where the operator surface 𝔏 : [ a , b ] × [ c , d ] → Φ 0 ( U , V ) {\mathfrak{L}:[a,b]\times[c,d]\to\Phi_{0}(U,V)} , ( λ , μ ) ↦ 𝔏 ( λ , μ ) {(\lambda,\mu)\mapsto\mathfrak{L}(\lambda,\mu)} , depends continuously on the perturbation parameter, μ, and holomorphically, as well as nonlinearly, on the spectral parameter, λ, where Φ 0 ( U , V ) {\Phi_{0}(U,V)} stands for the set of Fredholm operators of index zero between U and V. The main result is a substantial extension of a classical finite-dimensional theorem of T. Kato (see [T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Class. Math., Springer, Berlin, 1995, Chapter 2, Section 5]). |
| Databáze: | OpenAIRE |
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