International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 1, Pages 15-28
doi:10.1155/S0161171279000028

Strong boundedness of analytic functions in tubes

Abstract

Certain classes of analytic functions in tube domains TC=ℝn+iC in n-dimensional complex space, where C is an open connected cone in ℝn, 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′.