Skip to main content
Log in

On the approximation by entire functions of exponential type in \(L_{p,\alpha }(\mathbb {R})\)

  • Published:
Journal of Pseudo-Differential Operators and Applications Aims and scope Submit manuscript

Abstract

In this paper, we obtain the direct theorem of approximation of functions on the real line \(\mathbb {R}\) in the metric of \(L_{p}\) with some power weight using generalized Dunkl shifts.

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. Li, Y.P., Su, C.M., Ivanov, V.I.: Some problems of approximation theory in the spaces \(L_{p}\) on the line with power weight. Mat. Zametki 90(3), 362–383 (2011)

    Article  MathSciNet  Google Scholar 

  2. Nikol.skii, S.M.: Approximation of functions of several variables and embedding theorems, Nauka, Moscow (1969)

  3. Andersen, N.B., De Jeu, M.: Elementary proofs of Paley-Wiener theorems for the Dunkl transform on the real line. Int. Math. Res. Not. 30, 1817–1831 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Mejjaoli, H., Sraieb, N.: Uncertainty principles for the continuous Dunkl Gabor transform and the Dunkl continuous wavelet transform. Mediterr. J. Math. 5(4), 443–466 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Dunkl, C.F.: Integral kernels with re.ection group invariance. Can. J. Math. 43(6), 1213–1227 (1991)

    Article  MATH  Google Scholar 

  6. De Jeu, M.: The Dunkl transform. Invent. Math. 113(1), 147–162 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  7. Thangavelu, S., Xu, Y.: Convolution operator and maximal function for the Dunkl transform. J. Anal. Math. 97, 25–55 (2005)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. El Ouadih.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Daher, R., El Ouadih, S. On the approximation by entire functions of exponential type in \(L_{p,\alpha }(\mathbb {R})\) . J. Pseudo-Differ. Oper. Appl. 8, 341–347 (2017). https://doi.org/10.1007/s11868-016-0160-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11868-016-0160-1

Keywords

Navigation