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A remark on multivariate projection operators

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Abstract

This paper is a recapitulation of the work of L. Szili and P. Vértesi [4] on multivariate Fourier series with triangular type partial sums. Namely, we give another proof for the corresponding lower estimation, which, in a way, is more direct than the previous one in [4].

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References

  1. H. Berens and Y. Xu, Fejér means for multivariate Fourier series, Mat. Z., 221 (1996), 449–465.

    MathSciNet  MATH  Google Scholar 

  2. J. G. Herriot, Nörlund summability of multiple Fourier series, Duke Math. J., 11 (1944), 735–754.

    Article  MathSciNet  MATH  Google Scholar 

  3. E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press (Princeton, 1971).

    MATH  Google Scholar 

  4. L. Szili and P. Vértesi, On multivariate projection operators, J. Approx. Theory, 159 (2009), 154–164.

    Article  MathSciNet  MATH  Google Scholar 

  5. F. Weisz, l 1-summability of higher-dimensional Fourier series, J. Approx. Theory, 163 (2011), 99–116.

    Article  MathSciNet  MATH  Google Scholar 

  6. Y. Xu, Christoffel functions and Fourier series for multivariate orthogonal polynomials, J. Approx. Theory, 82 (1995), 205–239.

    Article  MathSciNet  MATH  Google Scholar 

  7. A. Zygmund, Trigonometric Series, Vol. I and Vol. II, Cambridge University Press (Cambridge, 1959).

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica, Universitá di Roma ‘La Sapienza’, Roma, Piazzale Aldo Moro 7, I-00185, Italy

    B. Della Vecchia

  2. Dipartimento di Matematica, Universitá della Basilicata, Potenza, Contrada Macchia Romana, I-85100, Italy

    G. Mastroianni

  3. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Reáltanoda u. 13–15, H-1053, Hungary

    P. Vértesi

Authors
  1. B. Della Vecchia
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  2. G. Mastroianni
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  3. P. Vértesi
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Correspondence to P. Vértesi.

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Della Vecchia, B., Mastroianni, G. & Vértesi, P. A remark on multivariate projection operators. Acta Math Hung 139, 337–343 (2013). https://doi.org/10.1007/s10474-012-0270-z

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  • DOI: https://doi.org/10.1007/s10474-012-0270-z

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