Strong boundedness of analytic functions in tubes - Richard D. Carmichael (International Journal of Mathematics and Mathematical Sciences)
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′.