Continuous generalized Hankel-Clifford wavelet transformation

Authors

  • V. R. Lakshmi Gorty Department Computer Engineering, SVKM’s NMIMS University, MPSTME, Vile-Parle (W), Mumbai -400056, India

Keywords:

Continuous Generalized Hankel-Clifford Wavelet Transformation, Generalized Hankel-Clifford Transformation, Generalized Hankel Convolution

Abstract

In this paper, the generalized Hankel-Clifford wavelet transformation is developed. Using the developed theory of generalized Hankel-Clifford convolution, the generalized Hankel-Clifford translation is introduced. Properties of the kernel Dμαβ(x,y,z) are developed in the study. Using the properties of kernel the generalized Hankel-Clifford wavelet transformation is defined. The existence of the generalized Hankel-Clifford wavelet transformation is given by a theorem. The boundedness and inversion formula for the generalized Hankel-Clifford wavelet transformation is obtained. A basic wavelet which defines continuous generalized Hankel-Clifford wavelet transformation, its admissibility conditions and the wavelet to the function is proved. Examples have been shown to explain the studied continuous generalized Hankel-Clifford wavelet transformation. MSC: 44A20, 42C40, 46

References

P. Malgonde, Feb.2000, On the generalized Hankel-Clifford integral transformation of generalized functions, Indian Journal of pure appl. Math., 31(2):197-206.

Kilbas, Anatoly A. , Trujillo, Juan J. , May 2003, "Hankel-Schwartz and Hankel-Clifford transforms on spaces", Results in Mathematics, 43, Issue 3-4, pp 284-299.

G. N. Watson, 1958, A treatise on the theory of Bessel functions, Cambridge University Press, London.

S. P. Malgonde G. S. Gaikawad; Nov.2001, On a generalized Hankel type convolution of generalized functions, Proc. Indian Acad. Sci. (Math.sci.), Vol.111, No.4, , pp.471-487.

A. H. Zemanian, 1968, Generalized Integral Transformations; Inter Science Publishers, N. Y.

D. T. Haimo, 1965, "Integral Equations Associated with Hankel convolutions", Trans. Amer. Math. Soc. 116, 33-375.

R. S. Pathak, 2009, The Wavelet Transform, Atlantis Studies in Mathematics for Engineering and Science: Atlantis Press, Vol. 4.

S. P. Malgonde, "Generalized Hankel-Clifford transformation of certain spaces of distributions", Rev. Acad. Canaria Cienc. 12(2000), 51-73.

R. S. Pathak and M. M. Dixit, "Continuous and discrete Bessel wavelet transforms", JOCAM, 160(2003), 241-250.

V. R. Lakshmi Gorty, "Continuous Hankel-Clifford wavelet transformation", Journal of Wavelet Theory and Applications, 7(1), (2013), 45-55.

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Published

2013-12-30

How to Cite

[1]
V. R. L. Gorty, “Continuous generalized Hankel-Clifford wavelet transformation”, Int. J. Comp. Sci. Eng., vol. 1, no. 4, pp. 1–10, Dec. 2013.

Issue

Vol. 1 No. 4 (2013): IJCSE December Edition

Section

Research Article

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