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

Byung Keun Sohn

International Journal of Mathematics and Mathematical Sciences, 2014, vol. 2014, 1-8

Abstract:

Let be a regular cone in and let be a tubular radial domain. Let be the convolutor in Beurling ultradistributions of -growth corresponding to . We define the Cauchy and Poisson integral of and show that the Cauchy integral of   is analytic in and satisfies a growth property. We represent   as the boundary value of a finite sum of suitable analytic functions in tubes by means of the Cauchy integral representation of . Also we show that the Poisson integral of corresponding to attains as boundary value in the distributional sense.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:926790

DOI: 10.1155/2014/926790

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