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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1969, Volume 6, Issue 4, Pages 417–424 (Mi mz6948)

The problem of conformal transformations of a circle into nonoverlapping regions

L. Kh. Burshtein

Leningrad State University named after A. A. Zhdanov

Abstract: Let $a$, $a\ne0$, $a\ne\infty$, be a fixed point in the $z$-plane, $\mathfrak M (a,0,\infty)$, the class of all systems $\{f_k(\zeta)\}_1^3$ of functions $z=f_k(\zeta)$, $k=1,2,3$, of which the first two map conformally and in a single-sheeted manner the circle $|\zeta|<1$, and the third maps in a similar manner the region $|\zeta|>1$, into pair-wise nonintersecting regions $B_k$, $k=1,2,3$, containing the points $a,0$, and $\infty$, respectively, so that $f_1(0)=a$, $f_2(0)=0$ and $f_3(\infty)=\infty$. The region of values $\mathscr E(a,0,\infty)$ of the system $M(|f_1'(0)|,|f_2'(0)|,1/|f_3'(0)|)$ in the class $\mathfrak M(a,0,\infty)$ is determined.

Full text: PDF file (529 kB)

English version:
Mathematical Notes, 1969, 6:4, 705–709

Bibliographic databases:

UDC: 517.5

Citation: L. Kh. Burshtein, “The problem of conformal transformations of a circle into nonoverlapping regions”, Mat. Zametki, 6:4 (1969), 417–424; Math. Notes, 6:4 (1969), 705–709

Citation in format AMSBIB
\Bibitem{Bur69}
\by L.~Kh.~Burshtein
\paper The problem of conformal transformations of a~circle into nonoverlapping regions
\jour Mat. Zametki
\yr 1969
\vol 6
\issue 4
\pages 417--424
\mathnet{http://mi.mathnet.ru/mz6948}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=252626}
\zmath{https://zbmath.org/?q=an:0195.36402|0186.40101}
\transl
\jour Math. Notes
\yr 1969
\vol 6
\issue 4
\pages 705--709
\crossref{https://doi.org/10.1007/BF01093806}