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A Wiener-Tauberian theorem for Fourier-Jacobi transform

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Approximation Theory and its Applications

Abstract

Let f∈Lp(R +, Δ(t)dt), we consider conditions under which the space spanned by generalized translates of f is dense in Lp(R +, Δ(t)dt) in terms of Fourier-Jacobi trans form of f. This generalizes and improves the earlier results of A. Sitaram on semi-simple Lie groups of rank one.

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References

  1. Ehrenpreis, L. and Mautner, F. I., Some Properties of the Fourier Transform on Semi-simple Lie groups, I, Ann. of Math., 61 (1995), 406–439.

    Article  MathSciNet  Google Scholar 

  2. Sitaram, A., An Analogue of the Wiener-Tauberian Theorem for Spherical Transforms on Semi-Simple Lie Groups, Pacific J. Math., 89 (1980), 439–445.

    Article  MathSciNet  Google Scholar 

  3. Sitaram, A., On an Analogue of the Wiener-Tauberian Theorem for Symmetric Spaces of the Non-Compact Type, Pacific J. Math., 133 (1988), 197–208.

    Article  MathSciNet  Google Scholar 

  4. Garnett, J. B., Bounded Analytic Functions, Academic Press, 1981.

  5. Koornwinder, T. H., Jacobi Functions and Analysis on Noncompact Semisimple Lie Groups, in R. Askey et al (eds.) Special Functions. D. Reidel Publishing Company. Dordrecht, Boston, Lancaster. 1984.

    MATH  Google Scholar 

  6. Flensted-Jensen, M., Paley-Wiener Type Theorems for a Differential Operator Connected with Symmetric Spaces. Ark. Mat. 10 (1972), 143–162.

    Article  MathSciNet  Google Scholar 

  7. Flensted-Jensen, M. and Koornwinder, T. H., The convolution Structure for Jacobi Function Expansions. Ark. Mat. 11 (173), 245–262.

    Article  MathSciNet  Google Scholar 

  8. Berhg, J. and Löfström, J., Interpolation Spaces, An introduction, Springer-Verlag, Berlin Heidelberg, New York, 1976.

    Google Scholar 

  9. Liu Jianming, and Zheng Weixing, The Decomposition of the RepresentationT o and the Plancheral Formula for the Universal Convering Group ofSU(1,1), Approximation Theory and its Application, to appear.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, 210093, Nanjing, China

    Liu Jianming & Zheng Weixing

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  1. Liu Jianming
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  2. Zheng Weixing
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Jianming, L., Weixing, Z. A Wiener-Tauberian theorem for Fourier-Jacobi transform. Approx. Theory & its Appl. 13, 97–104 (1997). https://doi.org/10.1007/BF02836265

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  • DOI: https://doi.org/10.1007/BF02836265

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