We pose and solve the Keldysh-Sedov problem: determine a function holomorphic in a bi-halfplane where its real and imaginary parts are given on mutually nonintersecting rectangles which exhaust the plane and which are the frame of the boundary of the bi-halfplane. Necessary and sufficient conditions for this problem to be solvable are given.
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Translated from Matematicheskii Zametki, Vol. 19, No. 5, pp. 681–690, May, 1976.
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Kakichev, V.A., Zon, L. The Keldysh-Sedov problem for functions holomorphic in a bi-halfplane. Mathematical Notes of the Academy of Sciences of the USSR 19, 410–415 (1976). https://doi.org/10.1007/BF01142561
- Imaginary Part