Some results concerning the analytic representation of distributions

Iseni, Egzona and Rushtimi, Agim and Rexhepi, Shpetim (2018) Some results concerning the analytic representation of distributions. Journal of Natural Sciences and Mathematics of UT, 3 (5-6). pp. 176-179. ISSN 2671-3039

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One property of distributions which is essentially different from the situation pertaining to locally integrating function is that distributions are infinitely differentiable. Every locally integrating function has a distributional derivative since it can be identified with a certain distribution. In contrast of classical analysis, a convergent sequence of distributions can always be differentiated and the resulting sequence converges to the derivative of the limit. The theory of Cauchy integral of distributions is motivated by the classical theory of the Cauchy integral. In the theory of distributional behaviour of analytic functions the following two topics are central: the representation of distributions in terms of boundary values of analytic functions and the representation of analytic functions in terms of distributions. In this paper we obtain some results related to boundary values of analytic representations of a sequence of distributions using Cauchy representation for distributions and analytic representations of distributions in different spaces. Arbitrary continuous complex valued function on real line cannot be analytically continued into the complex plane. It is possible to find a complex function which is analytic in a subset of complex plane and which represents the function by a jump arbitrarily close to the real axis.

Item Type: Article
Subjects: Q Science > Q Science (General)
Divisions: Faculty of Engineering, Science and Mathematics > School of Electronics and Computer Science
Depositing User: Unnamed user with email
Date Deposited: 05 Jun 2019 08:34
Last Modified: 05 Jun 2019 08:34

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