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AIMS Mathematics, 2017, 2(2): 305-314. doi: 10.3934/Math.2017.2.305. Research article

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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

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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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Keywords: Banach Space; Hilbert Space; Sobolev Space; Normed Vector Space

Citation: Onur Alp Ilhan, Shakirbay G. Kasimov. On the property of bases of multiple systems in Sobolev-Liouville classes. AIMS Mathematics, 2017, 2(2): 305-314. doi: 10.3934/Math.2017.2.305

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3. Gokhberg I.C., Kreyn M.G., Introduction to the Theory of Linear non Self-adjoint Operators in the Hilbert Space, Moscow: Nauka, 1969.
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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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Copyright Info: 2017, Onur Alp Ilhan, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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