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Solution of Integral Equations by Dunkl and Distributional Dunkl Transform


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1 Department of Mathematics, J. N. V. University, Jodhpur - 342 005, India
     

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The paper investigates the Dunkl transform and distributional Dunkl transform and the basic properties as convolution. The integral equations such as Volterra integral equation of first and second kind and Abel integral equation are solved by using dunkl transform. Further, solution obtained is considered in distributional sense by employing integral equations to distribution spaces and as well as using the distributional Dunkl transform for its solution.

Keywords

Dunkl Transform, Fourier Transform, Distribution Spaces, Volterra Integral Equation, Fredlom Integral Equation of Convolution Type, Convolution.
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  • Ayadi, S. and Ben Farah, S. Real Paley - wiener type theorems for the Dunkl transforms on S'(Rd), Ramanujan J. 19 (2009), 225-236.

  • Ben Said, Salem and Orsted, Bent The wave equation for Dunkl operators, Indag. Mathem., N.S., 16 (3-4) (2005), 351-391

  • Boujeddaine, M., Daher, R. and El-Hamma, M. Sobolev Spaces for Dunkl Operators on real line, Asia Pacic J. Math. 1 (2) (2014), 176-181

  • Dai, Fung and Xu Yaun, Analysis on h- Harmonics and Dunkl Transforms, Advance Courses in Mathematics CRM Barcelona, Birakhauser, New York (2015).

  • Dunkl, C. F. Dierential-difference operators associated to rejection groups, Trans. Amer. Math. Soc. 311 (1989), 167-183.

  • Estrada, R. and Kanwal, R.P., Singular Integral Equations, Birkhauser, Boston - Basel - Berlin (2000).

  • Loonker, Deshna and Banerji, P. K. On the solution of distributional Abel integral equation by distributional Sumudu Transform, Internat. J. Math. Math. Sci. 2011 (2011), 1-8 Article ID 480528.

  • Loonker, Deshna and Banerji, P. K. Solution of Integral Equations by Generalized Wavelet Transform, Bol. Soc. Paran. Mat. 33 (2) (2015), 89 -94

  • Mejjaoli, H and Trimeche, K. Hypoellipticity and hypoanaliticity associated with the Dunkl Laplacian. Integ. Transf. and Special Funct.15, No 6 (2004), 523-548.

  • Singh, Abhishek, Loonker, Deshna and Banerji, P. K. On Dunkl - Plancherel theorem for vector valued Boehmians, J. Indian Acad. Math. 36 (1) (2014), 41 - 58.

  • Singh, Abhishek and Banerji, P. K. Dunkl transform of tempered Boehmians, J. Indian Acad Math. 34 (2012), 9-18.

  • Singh, Abhishek and Banerji, P. K. Dunkl transform of integrable Boehmians, J. Rajasthan Acd, Phy. Sci. 10 (2) (2011), 169-176.


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  • Solution of Integral Equations by Dunkl and Distributional Dunkl Transform

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Authors

Deshna Loonker
Department of Mathematics, J. N. V. University, Jodhpur - 342 005, India

Abstract


The paper investigates the Dunkl transform and distributional Dunkl transform and the basic properties as convolution. The integral equations such as Volterra integral equation of first and second kind and Abel integral equation are solved by using dunkl transform. Further, solution obtained is considered in distributional sense by employing integral equations to distribution spaces and as well as using the distributional Dunkl transform for its solution.

Keywords


Dunkl Transform, Fourier Transform, Distribution Spaces, Volterra Integral Equation, Fredlom Integral Equation of Convolution Type, Convolution.

References