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Vestnik KRAUNC. Fiziko-Matematicheskie Nauki, 2022, Volume 39, Number 2, Pages 42–61
DOI: https://doi.org/10.26117/2079-6641-2022-39-2-42-61
(Mi vkam537)
 

MATHEMATICS

Note on the spectral theorem for unbounded non-selfadjoint operators

M. V. Kukushkin

Moscow State University of Civil Engineering
References:
Abstract: 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.
Keywords: Spectral theorem, Abel-Lidskii basis property, Schatten-von Neumann class, operator function, evolution equation.
Bibliographic databases:
Document Type: Article
UDC: 517.98
MSC: Primary 47B28; Secondary 47A10, 47B12, 47B10, 34K30, 58D25
Language: English
Citation: M. V. Kukushkin, “Note on the spectral theorem for unbounded non-selfadjoint operators”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 39:2 (2022), 42–61
Citation in format AMSBIB
\Bibitem{Kuk22}
\by M.~V.~Kukushkin
\paper Note on the spectral theorem for unbounded non-selfadjoint operators
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
\yr 2022
\vol 39
\issue 2
\pages 42--61
\mathnet{http://mi.mathnet.ru/vkam537}
\crossref{https://doi.org/10.26117/2079-6641-2022-39-2-42-61}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4484490}
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