Seminars: K. K. Rasulov, Continuation of separate analytical functions with fine features in each section

SEMINARS


Seminar on Modern Problems of Complex Analysis (Sadullaev Seminar) March 28, 2024 11:30, Tashkent, National University of Uzbekistan, Room A304 (Department of Mathematics)

Continuation of separate analytical functions with fine features in each section K. K. Rasulov National University of Uzbekistan named after M. Ulugbek, Tashkent
Abstract: Let $D\subset \mathbb{C}$ and $G\subset \mathbb{C}$ be bounded simply connected domains, $E\subset D$ and $F\subset G$ be regular compact sets. If $f(z,w)$ is a separate analytic function, with finite number of singular points in each section $D\times \{w\}$ and $\{z\}\times G$, $\forall (z, w)\in E\times F$, on the set $$ X=(D\times F)\bigcup (E\times G), $$ then it continues holomorphically into the domain $$ \hat{X} = \{(z,w)\in D\times G: {{\omega }^{}}(z,E,D)+{{\omega }^{}} (w,F,G)<1 \}, $$ except for some analytic set $S$. Here ${{\omega }^{}}(z,E,D)$ is the harmonic measure of the set $E\subset D\subset \mathbb{C}$ with respect to the domain $D$. Website:* https://us02web.zoom.us/j/8022228888?pwd=b3M4cFJxUHFnZnpuU3kyWW8vNzg0QT09