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Square Functions in the Theory of Cesàro Summability of Double Orthogonal Series

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Multivariate Approximation Theory III

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 75))

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Abstract

Let (X, F, μ) be a positive measure space, {ϕi (x): i= 0, 1, …} an orthonormal system (in abbreviation: ONS) defined on X, and {ai} a sequence of real numbers (coefficients).

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References

  1. Alexits, G. (1961) Convergence problems of orthogonal series ( Pergamon, Oxford )

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  2. Kaczmarz, S. (1925) Uber die Reiben von allgemeinen Orthogonalfunktionen. Math. Ann. 96, 148 – 151

    Article  Google Scholar 

  3. Kaczmarz, S. (1927) Uber die Summierbarkeit der Orthogonalreihan. Math. Z. 26, 99–105

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  4. Kolmogoroff, A.N. (1924) Une contribution a l’etude de la convergence des series de fourier. Fund Math. 5, 96 – 97

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  5. Menchoff, D.E. (1926) Sur les series de fonctions ortho-gonales II Fund Math 8, 56 - 108

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  6. Móricz, F. (1983) On the a. e. convergence of the arithmetic means of double orthogonal series. Trans. Amer. Math. Soc., submitted.

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  7. Móricz, F. (1985) On the (C, a≥0, ß≥0) -summability of double-orthogonal series. Studia Math., to appear

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  8. Móricz, F. and Tandori,. K. (1985) On the a. e. divergence of the arithmetic means of double orthogonal series. Studia Math., to appear

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  9. Tandori, K. (1985) Uber die Cesarosche Summierbarkeit von mehrfachen Orthogonalreihen. Acta Sci. Math. (Szeged), to appear

    Google Scholar 

  10. Zygmund, A. (1927) Sur l’application de la premiere moyenne arithmetique dans la theorie des series de fonctions orthogonales. Fund Math. 10, 356 – 362

    Google Scholar 

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© 1985 Birkhäuser Verlag Basel

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Móricz, F. (1985). Square Functions in the Theory of Cesàro Summability of Double Orthogonal Series. In: Schempp, W., Zeller, K. (eds) Multivariate Approximation Theory III. International Series of Numerical Mathematics, vol 75. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9321-3_29

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  • DOI: https://doi.org/10.1007/978-3-0348-9321-3_29

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9995-6

  • Online ISBN: 978-3-0348-9321-3

  • eBook Packages: Springer Book Archive

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