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Functional Means, Convolution Operators and Semigroups

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Differential Operators and Related Topics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 117))

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Abstract

The generalizations of Levy’s functional means are considered, which are the limits of integral means over the infinitely-divisible product-measures. Convolution operators with the family of such means form the C 0-semigroup generated by the non-Gaussian generalization of the Levy-Laplacian. The concentration of means near the sphere of a certain radius is verified. Behaviour of this radius in time is studied and its relation to the analytical properties of the operator semigroup. By way of application the action of convolutions on the finite-supported functions is described.

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References

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Author information

Authors and Affiliations

  1. ‘Kiev Polytechnic Institute’, National Technical University of Ukraine, pr. Pobedy, 37, Kiev, Ukraine

    S. V. Koshkin Postgraduate Student (Chair of Mathematical Methods of System Analysis)

Authors
  1. S. V. Koshkin Postgraduate Student
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Editor information

Editors and Affiliations

  1. Department of Theoretical Physics, University of Odessa, 270026, Odessa, Ukraine

    V. M. Adamyan

  2. Department of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Ramat Aviv, Israel

    I. Gohberg

  3. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    M. Gorbachuk  & V. Gorbachuk  & 

  4. Department of Mathematics, Vrije Universiteit, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    M. A. Kaashoek

  5. Department of Mathematics, Technical University of Vienna, Wiedner Hauptstrasse 8-10/1411, 1040, Vienna, Austria

    H. Langer

  6. Institute of Mathematics, Economics and Mechanics, Odessa State University, 270057, Dvoryanskaya str. 2, Odessa, Ukraine

    G. Popov

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© 2000 Springer Basel AG

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Koshkin, S.V. (2000). Functional Means, Convolution Operators and Semigroups. In: Adamyan, V.M., et al. Differential Operators and Related Topics. Operator Theory: Advances and Applications, vol 117. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8403-7_15

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  • DOI: https://doi.org/10.1007/978-3-0348-8403-7_15

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9552-1

  • Online ISBN: 978-3-0348-8403-7

  • eBook Packages: Springer Book Archive

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