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

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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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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

References

• 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.