[Turkmath:6780] Seminar "Analysis and Applied Mathematics"

[Allaberen Ashyralyev]

Dear All,
You are cordially invited to the  Weekly Online Seminar “Analysis and
Applied Mathematics” on
*Date*: Tuesday, November 26, 2024
*Time:* 14.00-15.00 (Istanbul) = 13.00-14.00 (Ghent) = 16.00-17.00 (Almaty)
*Place:* Zoom link:
https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaHlDaVYrN3l5bzJVQT09,
Conference ID: 667 827 0445, Access code: 1

*Speaker: Assoc. *Prof. Dr. Maksim V. Kukushkin
National Research University Higher School of Economics (HSE), Moscow,
Russia
Institute of Applied Mathematics and Automation, Russian Academy of
Sciences, Nalchik, Russia

*Title: * On the infinitesimality of the summation order in the
Abell-Lidskii sense for the trace class
*Abstract:*   In the recent century the problem of root vectors system
completeness related to non-selfadjoint operators is undergone a serious
attention by such mathematicians as Markus A.S. [16], [17], Lidskii V.B.
[14], Krein M.G. [7], Katsnelson V.E. [6], Matsaev V.I.[18], Agranovich
M.S. [2] and others. In consequence, there appeared a fundamental concept
in the framework of abstract spectral theory including propositions on
summation of spectral decompositions (series on root vectors) in a
generalized sense such as Abel-Lidskii, Riesz, Bari, senses [2],[5]. The
problem of decreasing the summation order in the Abell-Lidskii sense was
formulated by Lidskii V.B. 1962 [15] for a case corresponding to the self
adjoint elliptic operator perturbed by a non-selfadjoint operator. More
generally, the problem was considered by Katsnelson V.E. 1967 [3] for
perturbations of a positive self adjoint operator under the strong
subordination condition [19]. In 1994, Agaranovich M.S. proved that the
summation order can be decreased to some positive number in the case
corresponding to an operator with the numerical range of values contained
in the domain of the parabolic type [2] (what is an essential restriction
in comparison with the sectorial condition). However, a problem on the
lower bound of the summation order has still not been solved.
 *Abstracts and forthcoming talks can be found on our webpage*
https://sites.google.com/view/aam-seminars
With my best wishes
*Prof. Dr. Allaberen Ashyralyev *
*Department of Mathematics, Bahcesehir University,**34349**, Istanbul,
Turkiye*
*Peoples' Friendship University of Russia (RUDN University),** Ul Miklukho
Maklaya 6, Moscow 117198, Russian Federation *
*Institute of Mathematics and Mathematical Modelling, 050010, Almaty,
Kazakhstan*
*e-mail: allaberen.ashyralyev at bau.edu.tr
<allaberen.ashyralyev at neu.edu.tr> and **aallaberen at gmail.com
<aallaberen at gmail.com> *
 http://akademik.bahcesehir.edu.tr/web/allaberenashyralyev

https://sites.google.com/view/aam-seminars

https://ejaam.org/editorial.html

*https://icaam-online.org/ <https://icaam-online.org/>*

*https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1
<https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1>*
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