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Linear Combinations of Gammaoperators in L p — Spaces

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Abstract

In 1951 P.L. Butzer defined in his thesis linear combinations of Bernstein polynomials. This type of combinations was extended to other operators by several authors. In this paper we define special linear combinations of Gammaoperators and we will prove a global direct result and an equivalence theorem. The proofs are based on a remarkable connection between the derivatives of the kernel of Gammaoperators and Laguerre polynomials and moreover between the moments of the Gammaoperators and Laguerre polynomials.

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Authors and Affiliations

  1. Universitatea din Sibiu, Facultatea de Stiiunţe, Str. I.Ratiu nr.7, RO - 2400, Sibiu, Romania

    Alexandru Lupaş

  2. Universität Dortmund, Lehrstuhl VIII für Mathematik, Vogelpothsweg 87, D - 44221, Dortmund, Germany

    Detlef H. Mache, Volker Maier & Manfred W. Müller

Authors
  1. Alexandru Lupaş
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  2. Detlef H. Mache
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  3. Volker Maier
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  4. Manfred W. Müller
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Dedicated to Prof. Dr. P. L. Butzer on the occasion of his 70th birthday

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Lupaş, A., Mache, D.H., Maier, V. et al. Linear Combinations of Gammaoperators in L p — Spaces. Results. Math. 34, 156–168 (1998). https://doi.org/10.1007/BF03322046

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  • DOI: https://doi.org/10.1007/BF03322046

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