Strong boundedness of analytic functions in tubes

[摘要] Certain classes of analytic functions in tube domainsTC=ℝn+iCinn-dimensional complex space, whereCis an open connected cone inℝn, are studied. We show that the functions have a boundedness property in the strong topology of the space of tempered distributionsg′. 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 ofg′.

[学科分类] 数学（综合）