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Remark on a Regularized Trace Formula for m-Laplacian in a Punctured Domain

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Functional Analysis in Interdisciplinary Applications (FAIA 2017)

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Abstract

In this paper we extend results on regularized trace formulae which were established in [9, 10] for the Laplace and m-Laplace operators in a punctured domain with the fixed iterating order \(m\in \mathbb N\). By using techniques of Sadovnichii and Lyubishkin [21], the authors in the papers [9, 10] described regularized trace formulae in the spatial dimension \(d=2\). In this remark one is to be claimed that the formulae are also valid in the higher spatial dimensions, namely, \(2\le d \le 2m\). Also, we give the further discussions on a development of the analysis associated with the operators in punctured domains. This can be done by using so called ‘nonharmonic’ analysis.

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Acknowledgements

This research is partially supported by a grant from the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. 0773/GF4). This publication is supported by the target program 0085/PTSF-14 from the Ministry of Science and Education of the Republic of Kazakhstan.

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Authors and Affiliations

  1. Department of Mathematics, Imperial College London, Al-Farabi Kazakh National University, 71 Al-Farabi Ave., Almaty 050040 Kazakhstan, 180 Queen’s Gate, London, SW7 2AZ, UK

    Gulzat Nalzhupbayeva & Niyaz Tokmagambetov

Authors
  1. Gulzat Nalzhupbayeva
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  2. Niyaz Tokmagambetov
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Corresponding author

Correspondence to Niyaz Tokmagambetov .

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Editors and Affiliations

  1. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    Tynysbek Sh. Kalmenov

  2. Department of Mechanics and Mathematics, Kazakhstan Branch of Lomonosov Moscow State University, Astana, Kazakhstan

    Erlan D. Nursultanov

  3. Department of Mathematics, Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

  4. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    Makhmud A. Sadybekov

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Nalzhupbayeva, G., Tokmagambetov, N. (2017). Remark on a Regularized Trace Formula for m-Laplacian in a Punctured Domain. In: Kalmenov, T., Nursultanov, E., Ruzhansky, M., Sadybekov, M. (eds) Functional Analysis in Interdisciplinary Applications. FAIA 2017. Springer Proceedings in Mathematics & Statistics, vol 216. Springer, Cham. https://doi.org/10.1007/978-3-319-67053-9_25

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