scholarly journals Vector Valued Hyperfunctions and Boundary Values of Vector Valued Harmonic and Holomorphic Functions

2008 ◽  
Vol 44 (4) ◽  
pp. 1097-1142 ◽  
Author(s):  
Paweł Domański ◽  
Michael Langenbruch
Keyword(s):  
Holomorphic Functions ◽  
Boundary Values ◽  
Vector Valued

scholarly journals Bounded and Almost Periodic Ultradistributions as Boundary Values of Holomorphic Functions

2003 ◽  
Vol 33 (4) ◽  
pp. 1295-1311
Author(s):  
C. Fernández ◽  
A. Galbis ◽  
M.C. Gómez-Collado
Keyword(s):  
Holomorphic Functions ◽  
Almost Periodic ◽  
Boundary Values

scholarly journals Holomorphic extension of generalizations ofHpfunctions

1985 ◽  
Vol 8 (3) ◽  
pp. 417-424 ◽  
Author(s):  
Richard D. Carmichael
Keyword(s):  
Convex Hull ◽  
Extension Theorem ◽  
Holomorphic Functions ◽  
Holomorphic Extension ◽  
Finite Union ◽  
Convex Cones ◽  
Recent Analysis ◽  
Boundary Values ◽  
Connected Component ◽  
Open Convex

In recent analysis we have defined and studied holomorphic functions in tubes inℂnwhich generalize the HardyHpfunctions in tubes. In this paper we consider functionsf(z),z=x+iy, which are holomorphic in the tubeTC=ℝn+iC, whereCis the finite union of open convex conesCj,j=1,…,m, and which satisfy the norm growth of our new functions. We prove a holomorphic extension theorem in whichf(z),z ϵ TC, is shown to be extendable to a function which is holomorphic inT0(C)=ℝn+i0(C), where0(C)is the convex hull ofC, if the distributional boundary values in𝒮′off(z)from each connected componentTCjofTCare equal.

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