Quadratic-Phase Hankel Transformation and Calderón’s Reproducing Formula

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DOI:

https://doi.org/10.26713/cma.v15i2.2790

Keywords:

Hankel transformation, Quadratic-phase Hankel transformation, convolution, Calderón’s formula

Abstract

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

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References

A. P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Mathematica 24 (1964), 113 – 190, DOI: 10.4064/sm-24-2-113-190.

C. K. Chui, An Introduction to Wavelets, Academic Press, London, 278 pages (1992), DOI: 10.2307/2153134.

I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, Volume 61, SIAM, Philadelphia, xix + 357 pages (1992), DOI: 10.1137/1.9781611970104.

L. Debnath and F. A. Shah, Wavelet Transforms and Their Applications, 2nd edition, Birkhäuser, Boston, xv + 553 pages (2015), 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, Volume 79, American Mathematical Society (1991), DOI: 10.1090/cbms/079.

R. S. Pathak and G. Pandey, Calderón’s reproducing formula for Hankel convolution, International Journal of Mathematics and Mathematical Sciences 2006(1) (2006), Article ID 24217, DOI: 10.1155/IJMMS/2006/24217.

R. S. Pathak and M. M. Dixit, Continuous and discrete Bessel wavelet transforms, Journal of Computational and Applied Mathematics 160(1-2) (2003), 241 – 250, DOI: 10.1016/S0377-0427(03)00626-5.

M. A. Pinsky, Integrability of the continuum wavelet kernel, Proceedings of the American Mathematical Society 132(6) (2003), 1729 – 1737, DOI: 10.1090/S0002-9939-03-07253-8.

A. Prasad and T. Kumar, Canonical Hankel wavelet transformation and Calderón’s reproducing formula, Filomat 32(8) (2018), 2735 – 2743, DOI: 10.2298/FIL1808735P.

A. Prasad, T. Kumar and A. Kumar, Convolution for a pair of quadratic-phase Hankel transforms, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 114 (2020), Article number 150, DOI: 10.1007/s13398-020-00873-9.

S. K. Upadhyay and A. Tripathi, Calderón’s reproducing formula for Watson wavelet transform, Indian Journal of Pure and Applied Mathematics 46(3) (2015), 269 – 277, DOI: 10.1007/s13226-015-0137-4.

S. K. Upadhyay and R. Singh, Integrability of the continuum Bessel wavelet kernel, International Journal of Wavelets, Multiresolution and Information Processing 13(05) (2015), Article ID 1550032, DOI: 10.1142/S0219691315500320.

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Published

14-11-2024
CITATION

How to Cite

Roy, C., Kumar, T., Prasad, A., & Jha, G. K. (2024). Quadratic-Phase Hankel Transformation and Calderón’s Reproducing Formula. Communications in Mathematics and Applications, 15(2), 571–582. https://doi.org/10.26713/cma.v15i2.2790

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Research Article