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′.
Highlights
+ iC n, in n-dimensional complex space, where C is an open connected cone in are studied
We show that the functions have a boundedness property in the strong topology of the space of tempered distributions Ig
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 topology of 8’
Summary
We show that the functions have a boundedness property in the strong topology of the space of tempered distributions Ig. 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 8’. Analytic Function in Tube, Strong Boundedness, Tempered Distribos isibutional Boundary Value. T is the space of tempered distributions of Schwartz [2] and (i.i). C is an open cone, and analyzed the spectral functions of these analytic functions corresponding to C being an open connected cone The results of [3] have been incorporated into the book [i] of Vladlmirov [i, section 26.4]. We show that the analytic functions considered by Vladimirov in these results have boundedness properties in the strong topology of the space of tempered distributions.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
