A generalized 𝒯-transform for the Fourier-type functional and its applications

Abstract

The main purpose of this paper is to define a generalized $\mathcal{T}$-transform, is denoted by ${\mathcal{T}}_n$, on function space. This transform can be used to calculate various functionals which are not calculated in the previous paper. We then establish the existence of transform for Fourier-type functionals with some examples in quantum mechanics. Finally, we obtain some relationships for ${\mathcal{T}}_n$-transforms involving the generalized Cameron-Storvick theorem and the recurrence formulas for the ${\mathcal{T}}_n$-transform.

Keywords:

• $\mathcal{T}$-transform
• generalized Cameron-Storvick theorem
• Fourier-type functional
• recurrence formula

AMS Subject Classifications:

• Primary: 33E20
• 44A05

Acknowledgments

The authors would like to express their gratitude to the referees for their valuable comments and suggestions which have improved the original paper. The work was supported by the research fund of Dankook University in 2022.

Disclosure statement

No potential conflict of interest was reported by the author(s).