Abstract:
Unbounded perturbations of discrete operators are considered. Formulas for regularized traces are obtained, in which a finite number of corrections of the perturbation theory are used. An exact relation is established between the degree of subordination of a perturbation to the unperturbed operator and the number of corrections necessary for the existence of a finite formula of the trace. New estimates for the kernel norm of a resolvent of discrete operators are obtained.
Citation:
V. A. Sadovnichii, V. E. Podolskii, “Regularized traces of discrete operators”, Control, stability, and inverse problems of dynamics, Trudy Inst. Mat. i Mekh. UrO RAN, 12, no. 2, 2006, 162–177; Proc. Steklov Inst. Math. (Suppl.), 255, suppl. 2 (2006), S161–S177
\Bibitem{SadPod06}
\by V.~A.~Sadovnichii, V.~E.~Podolskii
\paper Regularized traces of discrete operators
\inbook Control, stability, and inverse problems of dynamics
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2006
\vol 12
\issue 2
\pages 162--177
\mathnet{http://mi.mathnet.ru/timm161}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2338255}
\zmath{https://zbmath.org/?q=an:1135.47031}
\elib{https://elibrary.ru/item.asp?id=12040746}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2006
\vol 255
\issue , suppl. 2
\pages S161--S177
\crossref{https://doi.org/10.1134/S0081543806060149}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33847000574}
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https://www.mathnet.ru/eng/timm161
https://www.mathnet.ru/eng/timm/v12/i2/p162
This publication is cited in the following 5 articles:
A. I. Kozko, “O nekotorykh priznakakh skhodimosti dlya znakopostoyannykh i znakochereduyuschikhsya ryadov”, Chebyshevskii sb., 18:1 (2017), 123–133
Abdelkader Intissar, “Regularized trace formula of magic Gribov operator on Bargmann space”, Journal of Mathematical Analysis and Applications, 437:1 (2016), 59
B. E. Kanguzhin, N. E. Tokmagambetov, “A regularized trace formula for a well-perturbed Laplace operator”, Dokl. Math., 91:1 (2015), 1
A. R. Aliev, A. S. Mohamed, “On the well-posedness of a boundary value problem for a class of fourth-order operator-differential equations”, Diff Equat, 48:4 (2012), 596
Sadovnichii V.A., Podol'skii V.E., “Traces of operators with a relatively compact perturbation”, Differential Equations, 44:5 (2008), 712–716
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