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On a generalized Hankel type convolution of generalized functions

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The classical generalized Hankel type convolution are defined and extended to a class of generalized functions. Algebraic properties of the convolution are explained and the existence and significance of an identity element are discussed.

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  1. Braaksma B L J and De Snoo H S V, Generalized translation operators associated with a singular differential operator, ordinary and partial differential equations,Dundee Conference, Lecture Notes in Math. (Berlin: Springer-Verlag) (1974) vol. 415, pp. 62–77

    Google Scholar 

  2. Cholewinski F M, Hankel complex inversion theory,Mem. Am. Math. Soc. 58 (1965)

  3. Delsarte J, Une extension nouvelle de la theorie des fonctions presque-periodiques de Bohr,Acta. Math. 69 (1938) 259–317

    Article  MATH  MathSciNet  Google Scholar 

  4. Hirschmann I I Jr, Variation diminishing Hankel transforms,J. Anal. Math. 8 (1960/61) 307–336

    Article  Google Scholar 

  5. Malgonde S P and Gaikawad G S, A mixed Parseval equation and the generalized Hankel type transformations,J. Indian Acad. Math. 22(2) (2000)

  6. Malgonde S P and Gaikawad G S, On the generalized Hankel type transformation of generalized functions (communicated for publication)

  7. Nussbaun A E, On functions positive definite relative to the orthogonal group and the representation of functions on Hankel-Stieltjes transforms,Trans. Am. Math. Soc. 175 (1973) 389–408

    Article  Google Scholar 

  8. Pinto J De Sousa, A generalised Hankel convolution,SIAM J. Math. Anal. 16(6) (1985) 1335–1346

    Article  MATH  MathSciNet  Google Scholar 

  9. Sneddon I N, The use of integral transforms (New York: Tata McGraw-Hill) (1979)

    Google Scholar 

  10. Watson G N, A Treatise on the Theory of Bessel functions (Cambridge: Cambridge Univ. Press) (1944)

    MATH  Google Scholar 

  11. Zemanian A H, Generalized Integral Transformations, (Interscience) (1966); republished by Dover, New York (1987)

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Malgonde, S.P., Gaikawad, G.S. On a generalized Hankel type convolution of generalized functions. Proc. Indian Acad. Sci. (Math. Sci.) 111, 471–487 (2001).

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