[Turkmath:7162] Weekly Online 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, June 17, 2025
*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: * Prof. Dr. Roland Duduchava
Victor Kupradze Institute of Mathematics, University of Georgia & A.
Razmadze Mathematical Institute, Tbilisi, Georgia
*Title: *  Spectral theory of convolution integro-differential operators on
monoids
  *Abstract:* The interval 𝑮 = (−1,1) turns into a Lie group under the
group operation 𝑥 ∘ 𝑦 ≔ (𝑥 + 𝑦)(1 + 𝑥𝑥)−1, 𝑥, 𝑦 ∈ 𝑮. Then 𝑴 =
[0,1) is a submonoid of 𝑮 (has the same binary operation 𝑥 ∘ 𝑦) and we
can induce the invariant Haar measure 𝑑𝜇𝑴 = (1 − 𝑥2)−1𝑑𝑑 and the
Fourier transformation ℱ𝑴 from 𝑮 to 𝑴. The main object of the
investigation is the convolution operator 𝑊𝑴,𝑎 ≔ 𝑟+𝑊𝑮,𝑎 0 ℓ+,
𝑊𝑮,𝑎 0 ≔ ℱ𝑮 −1𝑎ℱ𝑮 restricted from 𝑮. Theory of convolution operators
𝑊𝑴,𝑎 on the submonoid 𝑴 is much more complicated, but more rich and
important in applications (example of Wiener-Hopf equations on submonoid 𝑴
= [0, ∞) of the Lie group 𝑮 = (−∞, ∞) is a good example). Convolution
equation 𝑊𝑴,𝑠𝜑 = 𝑓 in the Generic Bessel potential space setting 𝑓 ∈
𝔾ℍ𝑝 𝑠−𝑟(𝑴, 𝑑𝜇𝑴), 𝜑 ∈ 𝔾ℍ𝑝 𝑠 (𝑴, 𝑑𝜇𝑴), 1 < 𝑝 < ∞, 𝑠, 𝑟 ∈
ℝ, has non-trivial Fredholm index and the Fredholmity and solvability
conditions for discontinuous symbols 𝑎(𝜉) depend on the parameters of the
spaces. We expose the full theory of such convolution integro-differential
equations: Fredholm property and solvability criteria, index formula.
Formulas for solutions are available through the factorization of the
symbol.  Attached here is the file of the abstract.
 *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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