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Two versions of fractional powers of Hankel-type transformations and pseudo-differential operators

  • Akhilesh Prasad
  • Kanailal Mahato
Article

Abstract

Two versions of the fractional powers of Hankel-type transformations are discussed on certain Zemanian type spaces. The operational formulae are developed. Pseudo-differential operators (p.d.o.) associated with the symbol a(xy) are defined. Integral representation of p.d.o. are obtained. Using the fractional Hankel convolution it is shown that the p.d.o. satisfy the \(L_{\nu ,\mu }^{1}\) norm inequality. Finally these Hankel-type transformations are used in the solution of some partial differential equations.

Keywords

Hankel transformation Pseudo-differential operator  Bessel type operator Zemanian space 

Mathematics Subject Classification

Primary 46F05 47G30 Secondary 35S05 46E10 46E35 

Notes

Acknowledgments

This work is supported by Indian School of Mines, Dhanbad, under Grant Number No. 613002/ISM JRF/Acad/2013-14.

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Copyright information

© Springer-Verlag Italia 2016

Authors and Affiliations

  1. 1.Department of Applied MathematicsIndian School of MinesDhanbadIndia

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