Generalized Integral Transforms via the Series Expressions

Hyun Soo Chung
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Hyun Soo Chung: Department of Mathematics, Dankook University, Cheonan 31116, Korea

Mathematics, 2020, vol. 8, issue 4, 1-17

Abstract: 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.

Keywords: generalized integral transform; kernel; Wiener-Itô-Chaos expansion; Riesz’s theorem; Hahn-Banach theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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