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Displaying similar documents to “Polya's theorem for non-entire functions”

The Taylor transformation of analytic functionals with non-bounded carrier

Grzegorz Łysik (1994)

Studia Mathematica

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Let L be a closed convex subset of some proper cone in ℂ. The image of the space of analytic functionals Q'(L) with non-bounded carrier in L under the Taylor transformation as well as the representation of analytic functionals from Q'(L) as the boundary values of holomorphic functions outside L are given. Multipliers and operators in Q'(L) are described.

Continuation of holomorphic solutions to convolution equations in complex domains

Ryuichi Ishimura, Jun-ichi Okada, Yasunori Okada (2000)

Annales Polonici Mathematici

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For an analytic functional S on n , we study the homogeneous convolution equation S * f = 0 with the holomorphic function f defined on an open set in n . We determine the directions in which every solution can be continued analytically, by using the characteristic set.