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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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.
Sitaram, A., An Analogue of the Wiener-Tauberian Theorem for Spherical Transforms on Semi-Simple Lie Groups, Pacific J. Math., 89 (1980), 439–445.
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.
Garnett, J. B., Bounded Analytic Functions, Academic Press, 1981.
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.
Flensted-Jensen, M., Paley-Wiener Type Theorems for a Differential Operator Connected with Symmetric Spaces. Ark. Mat. 10 (1972), 143–162.
Flensted-Jensen, M. and Koornwinder, T. H., The convolution Structure for Jacobi Function Expansions. Ark. Mat. 11 (173), 245–262.
Berhg, J. and Löfström, J., Interpolation Spaces, An introduction, Springer-Verlag, Berlin Heidelberg, New York, 1976.
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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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