The generalized Fourier convolution on time scales

In this paper, we deduct some properties of the Fourier transform on arbitrary time scales. We define the generalized shifting problem and we prove the existence of solutions. We define a generalized convolution on anarbitrary time scale and we deduct and prove the generalized convolution theorem.

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Bibliographic Details
Published inIntegral transforms and special functions Vol. 34; no. 3; pp. 211 - 227
Main Authors Georgiev, S. G., Darvish, V.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 04.03.2023
Taylor & Francis Ltd
Subjects
bilateral Laplace transform
Convolution
Fourier transform
Fourier transforms
generalized convolution
generalized shifting problem
Laplace transform
Time
Time scale
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Summary:In this paper, we deduct some properties of the Fourier transform on arbitrary time scales. We define the generalized shifting problem and we prove the existence of solutions. We define a generalized convolution on anarbitrary time scale and we deduct and prove the generalized convolution theorem.
ISSN:1065-2469
1476-8291
DOI:10.1080/10652469.2022.2105323