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Open AccessArticle

Generalized Integral Transforms via the Series Expressions

Department of Mathematics, Dankook University, Cheonan 31116, Korea
Mathematics 2020, 8(4), 539; https://doi.org/10.3390/math8040539
Received: 25 February 2020 / Revised: 30 March 2020 / Accepted: 2 April 2020 / Published: 6 April 2020
(This article belongs to the Special Issue Applications of Inequalities and Function Analysis)
From the change of variable formula on the Wiener space, we calculate various integral transforms for functionals on the Wiener space. However, not all functionals can be obtained by using this formula. In the process of calculating the integral transform introduced by Lee, this formula is also used, but it is also not possible to calculate for all the functionals. In this paper, we define a generalized integral transform. We then introduce a new method to evaluate the generalized integral transform for functionals using series expressions. Our method can be used to evaluate various functionals that cannot be calculated by conventional methods. View Full-Text
Keywords: generalized integral transform; kernel; Wiener-Itô-Chaos expansion; Riesz’s theorem; Hahn-Banach theorem generalized integral transform; kernel; Wiener-Itô-Chaos expansion; Riesz’s theorem; Hahn-Banach theorem
MDPI and ACS Style

Chung, H.S. Generalized Integral Transforms via the Series Expressions. Mathematics 2020, 8, 539.

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