Skip to main content
Log in

Pointwise convergence of strong summability on sphere

  • Published:
Approximation Theory and its Applications

Abstract

In this paper, strong summability of Cesàro means (of critical order) of Fourier-Laplace series on unit sphere is discussed. The Pointwise convergence conditions are established. The results of this paper are analogous to those of single and multiple Fourier series.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Müller, C., Spherical Harmonics, in: Lecutre Notes in Mathematics, 17, Springer-Verlag, 1966.

  2. Szegö, G., Orthogonal Polynomials, AMS Colloquium Publication, 1939.

  3. Wang Kunyang, Equiconvergent Operator of Cesàro Means on Sphere and its Applications, J Beijing Normal Univ. (NS), 29:2(1993),143–153.

    MATH  Google Scholar 

  4. Berens, H., Butzer, P. L. und Pawelke, S., Limitierungsverfahren von Reihen Mehrdimensionaler Kugelfuncktionen und Deren Saturationsverhalten, Publ. RIMS, Kyoto Univ. Ser. A, 4(1968), 201–268.

    MathSciNet  Google Scholar 

  5. Lu Shanzhen, Strong Summability of Spherical Bochner-Riesz Means (in Chinese), Chinese Science, Ser. A, 6(1984), 492–503.

    Google Scholar 

  6. Lu Shanzhen, Wang Kunyang, Bochner-Riesz Means, Publishing House of Beijing Normal University, 1988.

  7. Wang Fu-Traing, Strong Summability of Fourier Series, Duke Math. J. 12(1945), 77–87.

    Article  MATH  MathSciNet  Google Scholar 

  8. Wang Kunyang, Another Paper on Strong Summability of Multiple Fourier Series (in Chinese), Chinese Science Bulletin, 15(1987), 1124–1127.

    Google Scholar 

  9. Bonami, J. & Clerc, J. L., Sommes de Cesàro et multiplicateurs des développoments en harmonique sphériques, Trans. AMS, 183(1973), 223–263.

    Article  MATH  MathSciNet  Google Scholar 

  10. Wang Kunyang, Some Estimates for the Strong Approximation of Continuous Periodic Functions of two Variables by its Sums of Marcinkiewicz Type, J Beijing Normal University, 2(1981), 7–22.

    Google Scholar 

  11. Hardy, G. H., Littlewood, J. E., & Polya, G., Inequalities, Cambridge Univ. Press, 1934.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pu, Z. Pointwise convergence of strong summability on sphere. Approx. Theory & its Appl. 11, 1–10 (1995). https://doi.org/10.1007/BF02836574

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02836574

Keywords

Navigation