Zobrazeno 1 - 10
of 59
pro vyhledávání: '"Richard D. Carmichael"'
Autor:
Richard D. Carmichael
Publikováno v:
Axioms, Vol 12, Iss 11, p 1036 (2023)
Vector-valued analytic functions in Cn, which are known to have vector-valued tempered distributional boundary values, are shown to be in the Hardy space Hp,1≤p<2, if the boundary value is in the vector-valued Lp,1≤p<2, functions. The analysis of
Externí odkaz:
https://doaj.org/article/e820ea55a83841ab904c788699fce473
Autor:
Richard D. Carmichael
Publikováno v:
Axioms, Vol 11, Iss 8, p 392 (2022)
Using the historically general growth condition on scalar-valued analytic functions, which have tempered distributions as boundary values, we show that vector-valued analytic functions in tubes TC=Rn+iC obtain vector-valued tempered distributions as
Externí odkaz:
https://doaj.org/article/351d488e6bb24e60ac865f99a84a808b
Autor:
Richard D. Carmichael
Publikováno v:
Axioms, Vol 11, Iss 2, p 39 (2022)
We consider analytic functions in tubes Rn+iB⊂Cn with values in Banach space or Hilbert space. The base of the tube B will be a proper open connected subset of Rn, an open connected cone in Rn, an open convex cone in Rn, and a regular cone in Rn, w
Externí odkaz:
https://doaj.org/article/869fc7f8ee564994ad9f5cc076fc5a55
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 4, Iss 3, Pp 435-443 (1981)
Let C be an open convex cone in n dimensional real space Rn such that C¯ does not contain any entire straight line. We obtain a growth condition on functions in the Hardy spaces HP(TC), 1≤p≤∞, corresponding to the tube TC=Rn+iC in n dimensiona
Externí odkaz:
https://doaj.org/article/763c517d11fd491f953ac581cf3ffbf0
Autor:
Richard D. Carmichael, R. S. Pathak
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 10, Iss 3, Pp 417-431 (1987)
Initial and final value Abelian theorems for the Whittaker transform of functions and of distributions are obtained. The Abelian theorems are obtained as the complex variable of the transform approaches 0 or ∞ in absolute value inside a wedge regio
Externí odkaz:
https://doaj.org/article/0becc34f4f5848e49b945fcb2ac52192
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 3, Iss 3, Pp 575-581 (1980)
A class of analytic functions in tube domains TC=ℝn+iC in n-dimensional complex space, where C is an open connected cone in ℝn, which has been defined by V. S. Vladimirov is studied. We show that a previously obtained L2 growth estimate concernin
Externí odkaz:
https://doaj.org/article/d08a55b0c6d74ebaa15431c7b0e24925
Autor:
Richard D. Carmichael
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 2, Iss 1, Pp 15-28 (1979)
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 tem
Externí odkaz:
https://doaj.org/article/1333dfa90593401896337808ed95d751
Autor:
Richard D. Carmichael
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 8, Iss 3, Pp 417-424 (1985)
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 fin
Externí odkaz:
https://doaj.org/article/757b749bf1d74a48a920327d5783a705
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 4, Iss 1, Pp 67-88 (1981)
An initial (final) value Abelian theorem concerning transforms of functions is a result in which known behavior of the function as its domain variable approaches zero (approaches ∞) is used to infer the behavior of the transform as its domain varia
Externí odkaz:
https://doaj.org/article/051539302e144e248002dc71da209ccb
Autor:
Richard D. Carmichael
Publikováno v:
International Journal of Mathematics and Mathematical Sciences, Vol 10, Iss 1, Pp 1-8 (1987)
In a previous article we have obtained a holomorphic extension theorem (edge of the wedge theorem) concerning holomorphic functions in tubes in ℂn which generalize the Hardy Hp functions for the cases 1
Externí odkaz:
https://doaj.org/article/f5625711b4654d2ab24f93eb6e8b2c2a