Abstract
In recent analysis we have defined and studied holomorphic functions in tubes in ℂn which generalize the Hardy Hp functions in tubes. In this paper we consider functions f(z), z = x + iy, which are holomorphic in the tube TC = ℝn + iC, where C is the finite union of open convex cones Cj, j = 1, …, m, and which satisfy the norm growth of our new functions. We prove a holomorphic extension theorem in which f(z), z ϵ TC, is shown to be extendable to a function which is holomorphic in T0(C) = ℝn + i0(C), where 0(C) is the convex hull of C, if the distributional boundary values in 𝒮′ of f(z) from each connected component of TC are equal.
Highlights
M, and which satisfy the norm growth of our new functions
The purpoue of this paper is to prove a holomorphic extension theorem for functions which are holomorphic in a tube in and which satisfy a norm growth condition that generalizes the norm growth for Hp functions in tubes
The dual cone C* of a cone C is defined as C* {t
Summary
M, and which satisfy the norm growth of our new functions. We prove a holomorphic extension theorem in. In this paper we prove a holomorphic extension theorem (edge of the wedge theore for holomorphic functions in TC which satisfy (i.I) for y E C where C is a finite n; union of open convex cones in the extended function is holomorphic in TO(C) where A 0C Recall from section 1 that the dual cone (O(C))* is closed and convex and by hypothesis in this Theorem (0(C))* contains interior points and has an admissible set q = of vectors.
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 callMore From: International Journal of Mathematics and Mathematical Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
