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Displaying similar documents to “Interpolation of bounded sequences”

On holomorphic continuation of functions along boundary sections

S. A. Imomkulov, J. U. Khujamov (2005)

Mathematica Bohemica

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Let D ' n - 1 be a bounded domain of Lyapunov and f ( z ' , z n ) a holomorphic function in the cylinder D = D ' × U n and continuous on D ¯ . If for each fixed a ' in some set E D ' , with positive Lebesgue measure mes E > 0 , the function f ( a ' , z n ) of z n can be continued to a function holomorphic on the whole plane with the exception of some finite number (polar set) of singularities, then f ( z ' , z n ) can be holomorphically continued to ( D ' × ) S , where S is some analytic (closed pluripolar) subset of D ' × .