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Composition of Pseudo-Differential Operators Associated with Jacobi Differential Operator

  • Akhilesh Prasad
  • Manoj Kumar Singh
Research Article
  • 55 Downloads

Abstract

Using inverse Fourier–Jacobi transform two symbols are defined and two pseudo-differential operators (p.d.o.’s) \(\mathcal {P}_{\alpha ,\beta }(x,D) \) and \(\mathsf {Q}_{\alpha ,\beta } (x,D) \) are introduced. Composition of \(\mathcal {P}_{\alpha ,\beta }(x,D) \) and \(\mathsf {Q}_{\alpha ,\beta } (x,D) \) is defined. It is shown that the p.d.o.’s and composition of p.d.o.’s are bounded in a Sobolev type space. Some special cases are discussed.

Keywords

Pseudo-differential operator Fourier–Jacobi differential operators Jacobi function Fourier–Jacobi Convolution 

Mathematics Subject Classification

46F12 

Notes

Acknowledgements

The first author is supported by NBHM, Govt. of India, under Grant No. 2/48(14)/2011/R&D II/3501.

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Copyright information

© The National Academy of Sciences, India 2018

Authors and Affiliations

  1. 1.Department of Applied MathematicsIndian Institute of Technology (Indian School of Mines)DhanbadIndia
  2. 2.Department of Mathematics, St. Xavier’s CollegeRanchi UniversityRanchiIndia

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