Some Relationships for the Generalized Integral Transform on Function Space

Hyun Soo Chung
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Hyun Soo Chung: Department of Mathematics, Dankook University, Cheonan 3116, Korea

Mathematics, 2020, vol. 8, issue 12, 1-16

Abstract: In this paper, we recall a more generalized integral transform, a generalized convolution product and a generalized first variation on function space. The Gaussian process and the bounded linear operators on function space are used to define them. We then establish the existence and various relationships between the generalized integral transform and the generalized convolution product. Furthermore, we obtain some relationships between the generalized integral transform and the generalized first variation with the generalized Cameron–Storvick theorem. Finally, some applications are demonstrated as examples.

Keywords: generalized integral transform; generalized convolution product; bounded linear operator; Gaussian process; Cameron–Storvick theorem; translation theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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