Some Relationships for the Generalized Integral Transform on Function Space

• Main Author: Hyun Soo Chung
• Format: Article
• Language: English
• Published: MDPI AG 2020-12-01
• Series: Mathematics
• Subjects: generalized integral transform; generalized convolution product; bounded linear operator; Gaussian process; Cameron–Storvick theorem; translation theorem
• Online Access: https://www.mdpi.com/2227-7390/8/12/2246

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.