<div dir="ltr"><div>Dear All,<div><div dir="ltr"><div style="font-family:inherit;background-color:transparent;background-image:inherit;background-position:inherit;background-size:inherit;background-repeat:inherit;background-origin:inherit;background-clip:inherit;border-right:inherit;font-size:1.375rem;line-height:28px;margin:0px;padding:0px"><span style="background-color:transparent;font-size:small;font-family:inherit">You are cordially invited to the Weekly Online Seminar “Analysis and Applied Mathematics” on </span><span style="background-color:transparent;font-family:inherit;font-size:1.375rem"> </span></div><div style="font-family:inherit;background-color:transparent;background-image:inherit;background-position:inherit;background-size:inherit;background-repeat:inherit;background-origin:inherit;background-clip:inherit;border-right:inherit;font-size:1.375rem;line-height:28px;margin:0px;padding:0px"><b style="font-size:small">Date</b><span style="font-size:small">: Tuesday, November 26, 2024 </span></div></div><div dir="ltr"><b>Time:</b> 14.00-15.00 (Istanbul) = 13.00-14.00 (Ghent) = 16.00-17.00 (Almaty)<br><b>Place:</b> Zoom link: <a href="https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaHlDaVYrN3l5bzJVQT09" rel="noreferrer" target="_blank">https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaHlDaVYrN3l5bzJVQT09</a>, Conference ID: 667 827 0445, Access code: 1 </div><div dir="ltr"> </div><b>Speaker: Assoc. </b>Prof. Dr.
Maksim V. Kukushkin </div><div>National Research University Higher School of Economics (HSE), Moscow, Russia </div><div>Institute of Applied Mathematics and Automation, Russian Academy of Sciences,
Nalchik, Russia </div><div><br></div><div><b>Title: </b>
On the infinitesimality of the summation order in the
Abell-Lidskii sense for the trace class</div><div><b>Abstract:</b>
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.
</div><div><div><div dir="ltr"> <b>Abstracts and forthcoming talks can be found on our webpage</b></div><div dir="ltr"><div><div><div><div><div><a href="https://sites.google.com/view/aam-seminars" rel="noreferrer noreferrer" target="_blank">https://sites.google.com/view/aam-seminars</a><br>With my best wishes</div></div></div></div></div></div></div></div></div><div><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div style="font-size:12.8px"><b style="font-size:12.8px">Prof. Dr. Allaberen Ashyralyev </b></div><div><span style="font-size:small"><b>Department of Mathematics, Bahcesehir University,</b></span><b>34349</b><span style="font-size:small"><b>, Istanbul, Turkiye</b></span><b style="font-size:12.8px"> </b></div><div><div style="font-size:12.8px"><span style="font-size:12.8px"><b>Peoples' Friendship University of Russia (RUDN University),</b></span><b style="color:rgb(51,51,51);font-family:arial,helvetica,sans-serif;font-size:13px"> Ul Miklukho Maklaya 6, Moscow 117198, Russian Federation </b></div><div style="font-size:12.8px"><b style="font-size:12.8px">Institute of Mathematics and Mathematical Modelling, 050010, Almaty, Kazakhstan</b></div><div style="font-size:12.8px"><b style="font-size:12.8px">e-mail: <a href="mailto:allaberen.ashyralyev@neu.edu.tr" style="color:rgb(17,85,204)" target="_blank">allaberen.ashyralyev@bau.edu.tr</a> and </b><b style="font-size:12.8px"><a href="mailto:aallaberen@gmail.com" style="color:rgb(17,85,204)" target="_blank">aallaberen@gmail.com</a> </b></div><div style="font-size:12.8px"><b style="font-size:12.8px"> </b><a href="http://akademik.bahcesehir.edu.tr/web/allaberenashyralyev" style="color:rgb(0,86,179);margin:0px;padding:0px;border:0px;font-stretch:inherit;font-size:14px;line-height:inherit;font-family:Roboto,sans-serif;vertical-align:baseline" target="_blank">http://akademik.bahcesehir.edu.tr/web/allaberenashyralyev</a></div><div><p class="MsoNormal"><a href="https://sites.google.com/view/aam-seminars" target="_blank">https://sites.google.com/view/aam-seminars</a></p><p class="MsoNormal"><a href="https://ejaam.org/editorial.html" target="_blank">https://ejaam.org/editorial.html</a><br></p><p class="MsoNormal"><span style="font-size:12.8px"><b><u><a href="https://icaam-online.org/" target="_blank">https://icaam-online.org/</a></u></b></span><br></p></div></div><div><font color="#1155cc"><span style="font-size:12.8px"><b><a href="https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1" target="_blank">https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1<br></a></b></span><br></font></div></div></div></div></div></div></div></div></div></div></div></div></div></div>