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AIMS Mathematics

2017, Volume 2, Issue 2: 305-314. doi: 10.3934/Math.2017.2.305
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Research article

On the property of bases of multiple systems in Sobolev-Liouville classes

  • 1.
    Faculty of Education, University of Erciyes Melikgazi 38039, Kayseri, Turkey
  • 2.
    Mechanics and Mathematics Faculty, National University of Uzbekistan, Tashkent, Uzbekistan
  • Received: 13 November 2016 Accepted: 09 May 2017 Published: 11 May 2017

  • In the present work we consider the question of preservation of the baseness property for the system of vectors $\varphi = {\left\{ {{\varphi _n}} \right\}_{n \in {Z^N}}}$ in the Sobolev-Liouville and Besov classes at small perturbations with the purpose of the further application of obtained results to study decomposition on root vectors of differential operators.

    Citation: Onur AlpI LHAN, Shakirbay G. KASIMOV. On the property of bases of multiple systems in Sobolev-Liouville classes[J]. AIMS Mathematics, 2017, 2(2): 305-314. doi: 10.3934/Math.2017.2.305

    Related Papers:

  • In the present work we consider the question of preservation of the baseness property for the system of vectors $\varphi = {\left\{ {{\varphi _n}} \right\}_{n \in {Z^N}}}$ in the Sobolev-Liouville and Besov classes at small perturbations with the purpose of the further application of obtained results to study decomposition on root vectors of differential operators.


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    [1] Grothendieck A., Produits tensoriels topologiques et espaces nucleaires, Mem. Amer. Math. Soc., 16 (1955).
    [2] Enflo P., A counterexample to the approximation problem in Banach spaces, Acta Math., 130(1973), 309-317.
    [3] Gokhberg I. C. , Kreyn M. G. , Introduction to the Theory of Linear non Self-adjoint Operators in the Hilbert Space, Moscow: Nauka, 1969.
    [4] Gokhberg I.C., Markus A.S., Stability for bases of Banach and Hilbert spaces, Izvestiya AN MSSR., 5 (1962), 17-35.
    [5] Riesz F. , Sekyofalvi-Nad B. , Lectures on Functional Analysis, Moscow, "Mir", 1979.
    [6] Shakirbay G. Kasimov., On a Property of Bases in Banach and Hilbert Spaces, Malaysian Journal of Mathematical Sciences, 5 (2011), 229-240.
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  • © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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  • 1. 

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