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International Journal of Mathematics and Mathematical Sciences
Volume 2, Issue 1, Pages 15-28
http://dx.doi.org/10.1155/S0161171279000028

Strong boundedness of analytic functions in tubes

Department of Mathematics, Iowa State University, Ames 50011, Iowa, USA

Received 30 October 1978

Copyright © 1979 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Certain classes of analytic functions in tube domains TC=n+iC in n-dimensional complex space, where C is an open connected cone in n, are studied. We show that the functions have a boundedness property in the strong topology of the space of tempered distributions g. We further give a direct proof that each analytic function attains the Fourier transform of its spectral function as distributional boundary value in the strong (and weak) topology of g.