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Localization of the Spectral Expansions Associated with the Partial Differential Operators

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Mathematical Methods in Engineering

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 23))

Abstract

In this paper we discuss precise conditions of the summability and localization of the spectral expansions associated with various partial differential operators. In this we study the problems in the spaces of both smooth functions and singular distributions. We study spectral expansions of the distributions with the compact support and classify the distributions with the Sobolev spaces. All theorems are formulated in terms of the smoothness and degree of the regularizations.

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Acknowledgements

This research work is supported by IIUM FRGS 14 142 0383.

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Authors and Affiliations

  1. Faculty of Engineering, International Islamic University Malaysia, Kuala Lumpur, Malaysia

    Abdumalik Rakhimov

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  1. Abdumalik Rakhimov
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Correspondence to Abdumalik Rakhimov .

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Editors and Affiliations

  1. Department of Mathematics, Çankaya University, Ankara, Turkey

    Kenan Taş

  2. Department of Mathematics, Çankaya University, Ankara, Turkey

    Dumitru Baleanu

  3. Instituto Superior de Engenharia do Porto, Porto, Portugal

    J. A. Tenreiro Machado

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Rakhimov, A. (2019). Localization of the Spectral Expansions Associated with the Partial Differential Operators. In: Taş, K., Baleanu, D., Machado, J. (eds) Mathematical Methods in Engineering. Nonlinear Systems and Complexity, vol 23. Springer, Cham. https://doi.org/10.1007/978-3-319-91065-9_11

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  • DOI: https://doi.org/10.1007/978-3-319-91065-9_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91064-2

  • Online ISBN: 978-3-319-91065-9

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