Spectral properties of ordinary differential operators admitting special decompositions
| Autor: | Krzysztof Stempak |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
Computer Science::Information Retrieval Applied Mathematics 010102 general mathematics Friedrichs extension General Medicine Type (model theory) Composition (combinatorics) Space (mathematics) Differential operator 01 natural sciences Weak derivative 010101 applied mathematics Combinatorics Sobolev space 0101 mathematics Analysis Self-adjoint operator |
| Zdroj: | Communications on Pure & Applied Analysis. |
| ISSN: | 1553-5258 |
| DOI: | 10.3934/cpaa.2021054 |
| Popis: | We investigate spectral properties of ordinary differential operators related to expressions of the form \begin{document}$ D^{\epsilon}+a $\end{document} . Here \begin{document}$ a\in \mathbb{R} $\end{document} and \begin{document}$ D^{\epsilon} $\end{document} denotes a composition of \begin{document}$ \mathfrak{d} $\end{document} and \begin{document}$ \mathfrak{d}^+ $\end{document} according to the signs in the multi-index \begin{document}$ {\epsilon} $\end{document} , where \begin{document}$ \mathfrak{d} $\end{document} is a first order linear differential expression, called delta-derivative, and \begin{document}$ \mathfrak{d}^+ $\end{document} is its formal adjoint in an appropriate \begin{document}$ L^2 $\end{document} space. In particular, Sturm-Liouville operators that admit the decomposition of the type \begin{document}$ \mathfrak{d}^+\mathfrak{d}+a $\end{document} are considered. We propose an approach, based on weak delta-derivatives and delta-Sobolev spaces, which is particularly useful in the study of the operators \begin{document}$ D^{\epsilon}+a $\end{document} . Finally we examine a number of examples of operators, which are of the relevant form, naturally arising in analysis of classical orthogonal expansions. |
| Databáze: | OpenAIRE |
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