Quadratic-Phase Hankel Transformation and Calder`on's Reproducing Formula

Authors

  • Chandra Roy University Department of Mathematics, Vinoba Bhave University, Hazaribag, Jharkhand, India 825301
  • Tanuj Kumar Department of Mathematics, UPES, Dehradun-248007, Uttarakhand, INDIA.
  • Akhilesh Prasad Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad-826004
  • Govind Kumar Jha Department of Mathematics, Markham College of Commerce, Hazaribag-825301,

Keywords:

Hankel transformation, Quadratic-phase Hankel transformation, convolution, Calder`on's formula

Abstract

In this paper, we have explored fundamental properties of the quadratic-phase Hankel
transformation. Additionally, we have derived Calder`on's reproducing formula for quadratic-
phase Hankel convolution based on the theory of the quadratic-phase Hankel transformation.

Downloads

Download data is not yet available.

References

References

A. P. Calder`on, Intermediate spaces and interpolation, the complex method, Studia Math.,

:113-190, 1964. doi:10.4064/sm-24-2-113-190

C. K. Chui, An introduction to wavelets, Academic Press, London, 1992.

doi:10.2307/2153134

I. Daubechies, Ten lectures on wavelets, CBMS-NSF regional conference series in applied

mathematics, Vol. 61, SIAM, Philadelphia, 1992. doi:10.1137/1.9781611970104

L. Debnath and F. A. Shah, Wavelet transforms and their applications, Birkha ̈user, Boston,

doi:10.1007/978-0-8176-8418-1

M. Frazier, B. Jawerth and G. Weiss, Littlewood-Paley theory and the study of function

spaces, CBMS regional conference series in mathematics, Vol. 79, American Mathematical Society, Rhode Island, 1991.

doi:10.1090/cbms/079

A. Prasad, T. Kumar, A. Kumar, Convolution for a pair of quadratic-phase Hankel transforms. Rev. R. Acad. Cienc. Exactas F ́ıs. Nat. Ser.

A Math. RACSAM, 114, 150 (2020).doi:10.1007/s13398-020-00873-9

A. Prasad, T. Kumar, Canonical Hankel wavelet transformation and Calder`on's reproducing formula, Filomat, 32(8), 2735–2743, (2018).

doi:10.2298/FIL1808735P

R. S. Pathak and M. M. Dixit, Continuous and discrete Bessel wavelet transforms, J. Comput. Appl. Math., 160(1-2):241-250, 2003.

doi:10.1016/S0377-0427(03)00626-5

R. S. Pathak and G. Pandey, Calder`on's reproducing formula for Hankel convolution, Int. J. Math. Math. Sci., 2006 Art. ID. 24217 (7

pages), 2006. doi:10.1155/IJMMS/2006/24217

S. K. Upadhyay and R. Singh, Integrability of the continuum Bessel wavelet kernel, Int. J. Wavelets Multiresolut. Inf. Process. 13(05),

Art. ID. 1550032 (13 pages) 2015. doi:10.1142/S0219691315500320

S. K. Upadhyay and A. Tripathi, Calder`on's reproducing formula for Watson wavelet

transform, Indian J. Pure Appl. Math., 46(3):269-277, 2015. doi:10.1007/s13226-015-0137-4

M. A. Pinsky, Integrability of the continuum wavelet kernel, Proc. Amer. Math. Soc., 132(6):1729-1737, 2003. doi:10.1090/S0002-9939-

-07253-8

Published

14-11-2024

How to Cite

Roy, C., Kumar, T. ., Prasad, A. ., & Jha, G. K. (2024). Quadratic-Phase Hankel Transformation and Calder`on’s Reproducing Formula. Communications in Mathematics and Applications, 15(2). Retrieved from https://rgnpublications.com/journals/index.php/cma/article/view/2790

Issue

Vol. 15 No. 2 (2024)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.