Convolutions

Svetlin G. Georgiev ()
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Svetlin G. Georgiev: University of Sofia “St. Kliment Ohridski”, Department of Differential Equations Faculty of Mathematics and Informatics

Chapter Chapter 6 in Theory of Distributions, 2021, pp 165-194 from Springer

Abstract: Abstract In this chapter we define convolution of distributions. We deduct some of its basic properties. We prove that the convolution of distributions exists and it is well defined. We introduce a regularization of distributions. As applications of the convolution of distributions, we introduce fractional differentiation and integration. In the chapter are investigated the convolution algebras D ′ ( Γ + ) $$\mathcal {D}^{\prime }(\varGamma +)$$ and D ′ ( Γ ) $$\mathcal {D}^{\prime }(\varGamma )$$ .

Keywords: Convolution of distributions; Regularization of distributions; Fractional differentiation of a distribution; Fractional integration of a distribution (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-81265-2_6

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DOI: 10.1007/978-3-030-81265-2_6

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