International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 3, Pages 417-424
Holomorphic extension of generalizations of functions
Department of Mathematical Sciences, New Mexico State University, Las Cruces 88003, New Mexico, USA
Received 31 March 1985
Copyright © 1985 Richard D. Carmichael. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In recent analysis we have defined and studied holomorphic functions in tubes in which generalize the Hardy functions in tubes. In this paper we consider functions , , which are holomorphic in the tube , where is the finite union of open convex cones , , and which satisfy the norm growth of our new functions. We prove a holomorphic extension theorem in which , , is shown to be extendable to a function which is holomorphic in , where is the convex hull of , if the distributional boundary values in of from each connected component of are equal.