Radon Transform Continuous on Schwartz Space

• Published: 09 September 2022

Fractional Hankel wavelet transform on the Schwartz type space

Journal of Pseudo-Differential Operators and Applications volume 13, Article number:48 (2022) Cite this article

Abstract

In this paper, we extend the fractional Hankel wavelet transformation to tempered distributions through the adjoint method. A suitable Schwartz type space is introduced and the continuity of this transform is proved in this space. Through this continuity, it is extended to its corresponding dual space of tempered distribution. The continuity and extension of the inverse of this transform is also proved. Some examples of distributions and application in differential equation are given. The solutions of the differential equation are plotted as graphs using matlab.

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Funding

This work is supported by the Scientific Engineering Research Board (SERB) under the core research grant scheme from the Department of Science and Technology, India (File No. CRG/2018/002491). The corresponding author is the recipient of this project.

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Authors and Affiliations

1. Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidhyapeetham, Coimbatore, India

   M. Thanga Rejini & R. Subash Moorthy

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Correspondence to R. Subash Moorthy.

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Thanga Rejini, M., Subash Moorthy, R. Fractional Hankel wavelet transform on the Schwartz type space. J. Pseudo-Differ. Oper. Appl. 13, 48 (2022). https://doi.org/10.1007/s11868-022-00482-7

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• Received: 23 May 2022

• Revised: 23 May 2022

• Accepted: 26 August 2022

• Published: 09 September 2022

• DOI : https://doi.org/10.1007/s11868-022-00482-7

Keywords

• Hankel translation and dilation
• Fractional Hankel wavelet
• Schwartz space
• Tempered distributions

Mathematics Subject Classification

• 44A15
• 46F12
• 42F12

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