Modern Problems of Complex Analysis (Sadullaev Seminar)

Time: Thursdays at 12:00 PM. 

Organizers:

 Gulmirza Khudayberganov
Karim Rakhimov
Bakhodir Shoimkulov
Isroil Ikromov
Alimardon Atamuratov


Scientific Secretary of the Seminar:
Jasurbek Karimov

Modern Problems of Complex Analysis (Sadullaev Seminar)

Talks

 16 October 2025 —  Sharipova Mubina (Bukhara State University) — on-site & online
Title: Estimates for the spectrum of a third-order operator matrix with a parameter
Abstract: In this talk, we propose an alternative formula for computing the cubic numerical range of bounded self-adjoint  3×3 operator matrices. We describe the essential and discrete spectra of a third-order operator matrix in Fock space. Furthermore, we establish a spectral inclusion for the spectra of the block elements. Finally, using the cubic numerical range, Gershgorin’s theorem, and classical perturbation theory, we obtain spectral estimates for this operator matrix.

09  October 2025  — Waldo Arriagada (New Uzbekistan University)— on-site & online
Title: On fractals and Math and the Arts

Abstract: In this talk we visit the read-Bajraktarević operator and its complex counterpart, and we visit some applications to Escher's 1956 famous lithography.

 2 October 2025 —  Kobiljon Kuldashev (National University of Uzbekistan) — on-site & online
Title : Weighted m-subharmonic measures.
Abstract: In this talk, we study weighted m-subharmonic measures within the class of m-subharmonic functions. We investigate their fundamental properties and establish several theorems on (m,ψ,δ)-regularity. In particular, we prove that if the weighted (m,ψ,δ)-subharmonic measure is Hölder continuous with respect to a compact set, then it is Hölder continuous in D; this result is novel even in the unweighted case. We also introduce the concepts of (m,ψ,δ)-capacity and weighted P(m,ψ,δ)-capacity and establish their basic properties.


25 September 2025 — Nurali Akramov (National University of Uzbekistan)— on-site & online
Title: Capacity dimensions of Brjuno and Perez-Marco sets.
Abstract: In this talk, we refine the result of Sadullaev–Rakhimov on the capacity dimension of the complement of the Brjuno set. Likewise, we obtain an improved result concerning the capacity dimension of the Pérez–Marco set.


18 September 2025 — Bukharbay Kurbanov (Karakalpak State University)— on-site & online
Title: Integral formulas and problems of holomorphic extension from the boundary in Siegel domains.

Abstract. The purpose of this study is to construct an analogue of the Cayley transform for matrix domains, to describe the automorphism groups of Siegel domains, to obtain explicit formulas for the kernels of the Bergman, Cauchy–Szegő, and Poisson integrals, and to establish sufficient conditions for holomorphic extension from the boundary of a Siegel domain in the form of Morera-type theorems.

4 September 2025 —  Kobiljon Kuldashev (National University of Uzbekistan) — on-site & online

Title: On the Hölder regularity of weighted 𝑚-subharmonic measures
Abstract: In this talk, we study the Hölder continuity properties of weighted 𝑚 −subharmonic measure of a compact set 𝐾  in the class of 𝑚−subharmonic functions. We prove that if the weighted 𝑚−subharmonic measure of 𝐾  is Hölder continuous with respect to 𝐾 and the weight function also satisfies the Hölder continuity condition on 𝐾, then it is Hölder continuous everywhere. Similarly, we show that if the above conditions are satisfied for the weighted 𝑚−Green function of 𝐾 , then it is also Hölder continuous everywhere.  This is a joint work with Karim Rakhimov.