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Spaces of Generalised Smoothness in Summability Problems for Φ-Means of Spectral Decomposition

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Book cover Current Trends in Analysis and Its Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

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Abstract

We establish conditions for localization of generalised Riesz means of spectral decomposition by system of fundamental functions of Laplace operator in terms of belongingness of the decomposing function to the spaces of generalised smoothness.

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References

  1. M.L. Goldman, T.G. Ayele, Spaces of generalised smoothness in problems of summability of spectral decompositions. All-Union Institute of Scientific and Technical Information, Russian Academy of Sciences 31.03.99 No. 1028-B99, Moscow

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  2. M.L. Goldman, Issledobanye prostranstb differentserumikh funktsii mnogikh peremenikh c obovshonoy gladcostyu. Dissertatsiya na soeskaniya ychonoy stepin doktora Fiziko-Matematichiskikh Nauk (1987)

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  3. M.L. Goldman, Abovshonie yadra drobnovo porydka. Differ. Uravn. 7(12), 1236–1255 (1971)

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  4. V.A. Ilin, Sh.A. Alimov, Conditions for the convergence of spectral decompositions that correspond to self-adjoint extensions of elliptic operators. I, II. Differ. Uravn. 7, 670–710 (1971); 851–882

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Acknowledgement

This Research was supported by Humboldt Foundation Research Fellowship Grant No. 3.4-ATH/1144171 in the case of the first author.

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Authors and Affiliations

  1. Department of Mathematics, Addis Ababa University, P.O. Box 1176, Addis Ababa, Ethiopia

    Tsegaye G. Ayele

  2. Department of Nonlinear Analysis and Optimization, Peoples’ Friendship University of Russia, Miklukho-Maklaya str. 6, Moscow, 117198, Russia

    Mikhail L. Goldman

Authors
  1. Tsegaye G. Ayele
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  2. Mikhail L. Goldman
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Corresponding author

Correspondence to Tsegaye G. Ayele .

Editor information

Editors and Affiliations

  1. Dept. of Computer Sc. & Comp. Methods, Pedagogical University, Kraków, Poland

    Vladimir V. Mityushev

  2. Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

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Ayele, T.G., Goldman, M.L. (2015). Spaces of Generalised Smoothness in Summability Problems for Φ-Means of Spectral Decomposition. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_20

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