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A norm of partial sums of Fourier-Jacobi series for functions from L (α,β) p

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Abstract

Asymptotic estimates for a norm of partial sums of Fourier-Jacobi series of functions from L (α,β) p are obtained.

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References

  1. H. Pollard, “The Mean Convergence of Orthogonal Series III,” Duke Math. J. 16(1), 189 (1949).

    Article  MATH  MathSciNet  Google Scholar 

  2. J. Levesley and A. K. Kushpel, “On the Norm of the Fourier-Jacobi Projection,” Numer. Funct. Anal. and Optim. 22(7–8), 941 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  3. G. Szego, Orthogonal Polynomials (AMS, Providence, RI, 1975; Nauka, Moscow 1962).

    Google Scholar 

  4. G. Gasper, “Positivity and the Convolution Structure for Jacobi Series,” Ann. Math. 93(1), 112 (1971).

    Article  MathSciNet  Google Scholar 

  5. G. Gasper, “Banach Algebra for Jacobi Series and Positivity of a Kernel,” Ann. Math. 95(2), 261 (1972).

    Article  MathSciNet  Google Scholar 

  6. H. Pollard, “The Mean Convergence of Orthogonal Series II,” Trans. Amer. Math. Soc. 63, 355 (1948).

    Article  MATH  MathSciNet  Google Scholar 

  7. I. K. Daugavet and S. Z. Rafal’son, “Some Inequalities of Markov-Nikol’skii Type for Algebraic Polynomials,” Vestn. Leningr. Univ. No 1, 15 (1972).

    Google Scholar 

  8. N. K. Bari, “A Generalization of the Inequalities of S. N. Bernstein and A. A. Markov,” Izv. Akad. Nauk SSSR, ser. Matem. 18,160 (1954).

    MathSciNet  Google Scholar 

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Original Russian Text © A.I. Kamzolov, 2007, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2007, Vol. 62, No. 6, pp. 17–25.

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Kamzolov, A.I. A norm of partial sums of Fourier-Jacobi series for functions from L (α,β) p . Moscow Univ. Math. Bull. 62, 228–236 (2007). https://doi.org/10.3103/S0027132207060034

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  • DOI: https://doi.org/10.3103/S0027132207060034

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