Note on the spectral theorem for unbounded non-selfadjoint operators

Autor:	Kukushkin, M.V.
Jazyk:	English<br />Russian
Rok vydání:	2022
Předmět:	spectral theorem abel-lidskii basis property schatten-von neumann class operator function evolution equation базисное свойство абеля-лидского класс шаттена-фон неймана оператор функция эволюционное уравнение Science
Zdroj:	Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, Vol 2022, Iss 2, Pp 42-61 (2022)
Druh dokumentu:	article
ISSN:	2079-6641 2079-665X
DOI:	10.26117/2079-6641-2022-39-2-42-61
Popis:	In this paper, we deal with non-selfadjoint operators with the compact resolvent. Having been inspired by the Lidskii idea involving a notion of convergence of a series on the root vectors of the operator in a weaker – Abel-Lidskii sense, we proceed constructing theory in the direction. The main concept of the paper is a generalization of the spectral theorem for a non-selfadjoint operator. In this way, we come to the definition of the operator function of an unbounded non-selfadjoint operator. As an application, we notice some approaches allowing us to principally broaden conditions imposed on the right-hand side of the evolution equation in the abstract Hilbert space.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/3419f8baa8cc453086f9916b54bc8dea Zobrazit plný text záznamu View record in DOAJ