Cauchy and Poisson Integral of the Convolutor in Beurling Ultradistributions of Lp-Growth

Cauchy and Poisson Integral of the Convolutor in Beurling Ultradistributions of Lp-Growth

Let C be a regular cone in ℝ and let TC=ℝ+iC⊂ℂ be a tubular radial domain. Let U be the convolutor in Beurling ultradistributions of Lp-growth corresponding to TC. We define the Cauchy and Poisson integral of U and show that the Cauchy integral of  U is analytic in TC and satisfies a growth property...

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Main Author: Byung Keun Sohn
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2014/926790
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spelling doaj-9c6f9afc95c7473e94632b8bc1d09b7e2020-11-24T22:27:51ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252014-01-01201410.1155/2014/926790926790Cauchy and Poisson Integral of the Convolutor in Beurling Ultradistributions of Lp-GrowthByung Keun Sohn0Department of Mathematics, Inje University, Gimhae 621-749, Gyeongnam, Republic of KoreaLet C be a regular cone in ℝ and let TC=ℝ+iC⊂ℂ be a tubular radial domain. Let U be the convolutor in Beurling ultradistributions of Lp-growth corresponding to TC. We define the Cauchy and Poisson integral of U and show that the Cauchy integral of  U is analytic in TC and satisfies a growth property. We represent  U as the boundary value of a finite sum of suitable analytic functions in tubes by means of the Cauchy integral representation of U. Also we show that the Poisson integral of U corresponding to TC attains U as boundary value in the distributional sense.http://dx.doi.org/10.1155/2014/926790
collection DOAJ
language English
format Article
sources DOAJ
author Byung Keun Sohn
spellingShingle Byung Keun Sohn
Cauchy and Poisson Integral of the Convolutor in Beurling Ultradistributions of Lp-Growth
International Journal of Mathematics and Mathematical Sciences
author_facet Byung Keun Sohn
author_sort Byung Keun Sohn
title Cauchy and Poisson Integral of the Convolutor in Beurling Ultradistributions of Lp-Growth
title_short Cauchy and Poisson Integral of the Convolutor in Beurling Ultradistributions of Lp-Growth
title_full Cauchy and Poisson Integral of the Convolutor in Beurling Ultradistributions of Lp-Growth
title_fullStr Cauchy and Poisson Integral of the Convolutor in Beurling Ultradistributions of Lp-Growth
title_full_unstemmed Cauchy and Poisson Integral of the Convolutor in Beurling Ultradistributions of Lp-Growth
title_sort cauchy and poisson integral of the convolutor in beurling ultradistributions of lp-growth
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2014-01-01
description Let C be a regular cone in ℝ and let TC=ℝ+iC⊂ℂ be a tubular radial domain. Let U be the convolutor in Beurling ultradistributions of Lp-growth corresponding to TC. We define the Cauchy and Poisson integral of U and show that the Cauchy integral of  U is analytic in TC and satisfies a growth property. We represent  U as the boundary value of a finite sum of suitable analytic functions in tubes by means of the Cauchy integral representation of U. Also we show that the Poisson integral of U corresponding to TC attains U as boundary value in the distributional sense.
url http://dx.doi.org/10.1155/2014/926790
work_keys_str_mv AT byungkeunsohn cauchyandpoissonintegraloftheconvolutorinbeurlingultradistributionsoflpgrowth
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