Orthonormal series expansion and finite spherical Hankel transform of generalized functions

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DOI:

https://doi.org/10.26637/mjm102/010

Abstract

The finite spherical Hankel transformation is extended to generalized functions by using orthonormal series expansion of generalized functions. A complete orthonormal family of spherical Bessel functions is derived and certain spaces of testing functions and generalized functions are defined. The inversion and uniqueness theorems are obtained. The operational transform formula is derived and is applied to solve the problem of the propagation of heat released from a spherically symmetric point heat source.

Keywords:

Finite spherical Hankel transform, orthonormal series expansion of generalized functions

Mathematics Subject Classification:

46F12, 44A15, 46F10, 41A58
  • S.K. Panchal Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431 004, (M.S.) India.
  • Pages: 77-82
  • Date Published: 01-04-2013
  • Vol. 1 No. 02 (2013): Malaya Journal of Matematik (MJM)

I. Isaac, H. Chen, Modified Fourier-Bessel Series and finite Spherical Hankel Transform, Int. J. Math.Educ. Sci. Technology, 13(3)(1982), 281–283. DOI: https://doi.org/10.1080/0020739820130307

A. H. Zemanian, Orthonormal series expansions of certain distributions and distributional transform calculus, J. Math. Anal. Appl., 14(1966), 263–275. DOI: https://doi.org/10.1016/0022-247X(66)90026-6

S. D. Bhosale and S. V. More, On Marchi-Zgrablich transformation of generalized functions, IMA J. Appl. Maths., 33(1984), 33–42. DOI: https://doi.org/10.1093/imamat/33.1.33

S. K. Panchal and S. V. More, On modified Marchi-Zgrablich transformation of generalized functions, J. Indian Acad. Math., 17(1)(1995), 13–26.

A. H. Zemanian, Generalized Integral Transformations, Interscience Publisher, New York, 1968.

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Published

01-04-2013

How to Cite

S.K. Panchal. “Orthonormal Series Expansion and Finite Spherical Hankel Transform of Generalized Functions”. Malaya Journal of Matematik, vol. 1, no. 02, Apr. 2013, pp. 77-82, doi:10.26637/mjm102/010.

Issue

Vol. 1 No. 02 (2013): Malaya Journal of Matematik (MJM)

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Articles

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Copyright (c) 2013 MJM

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