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Complete Asymptotic Expansions for Altomare Operators

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Abstract

In the present paper, we study an approximation process by a sequence of operators with a prescribed asymptotic behavior. The method of construction of these operators is due to Altomare and Amiar. The operators have several applications in semigroup theory. Our investigation provides an insight in their asymptotic behaviour. Finally, we apply our results to concrete examples of approximation operators recently defined and used by Altomare and Milella for the study of semigroups.

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Authors and Affiliations

  1. Fachbereich MND, Technische Hochschule Mittelhessen, Wilhelm-Leuschner-Straße 13, 61169, Friedberg, Germany

    Ulrich Abel

  2. Department of Mathematics, Technical University of Cluj-Napoca, Str. Memorandumului 28, 400114, Cluj-Napoca, Romania

    Mircea Ivan

Authors
  1. Ulrich Abel
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  2. Mircea Ivan
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Correspondence to Ulrich Abel.

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Dedicated to the 60th birthday anniversary of Prof. Francesco Altomare

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Abel, U., Ivan, M. Complete Asymptotic Expansions for Altomare Operators. Mediterr. J. Math. 10, 17–29 (2013). https://doi.org/10.1007/s00009-012-0183-7

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  • DOI: https://doi.org/10.1007/s00009-012-0183-7

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