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 APM  Vol.4 No.11 , November 2014
On Invertibility of Functional Operators with Shift in Weighted Hölder Spaces
Anna Tarasenko1*, Oleksandr Karelin2
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Abstract: In this paper, we consider functional operators with shift in weighted H?lder spaces. We present the main idea and the scheme of proof of the conditions of invertibility for these operators. As an application, we propose to use these results for solution of equations with shift which arise in the study of cyclic models for natural systems with renewable resources.
Keywords: Functional Operator with Shift, Hölder Space, Conditions of Invertibility, Renewable Resources
Cite this paper: Tarasenko, A. and Karelin, O. (2014) On Invertibility of Functional Operators with Shift in Weighted Hölder Spaces. Advances in Pure Mathematics, 4, 595-600. doi: 10.4236/apm.2014.411068.
References

[1]   Karlovich, Y.I. and Kravchenko, V.G. (1981) Singular Integral Equations with Non-Carleman Shift on an Open Contour. Differential Equations, 17, 2212-2223.

[2]   Litvinchuk, G.S. (2000) Solvability Theory of Boundary Value Problems and Singular Integral Equations with Shift. Kluwer Academic Publishers, Dordrecht, Boston, London. http://dx.doi.org/10.1007/978-94-011-4363-9

[3]   Kravchenko, V.G. and Litvinchuk, G.S. (1994) Introduction to the Theory of Singular Integral Operators with Shift. Kluwer Academic Publishers, Dordrecht, Boston, London. http://dx.doi.org/10.1007/978-94-011-1180-5

[4]   Tarasenko, A., Karelin, A., Lechuga, G.P. and Hernández, M.G. (2010) Modelling Systems with Renewable Resources Based on Functional Operators with Shift. Applied Mathematics and Computation, 216, 1938-1944.
http://dx.doi.org/10.1016/j.amc.2010.03.023

[5]   Karelin, O., Tarasenko, A. and Hernández, M.G. (2013) Application of Functional Operators with Shift to the Study of Renewable Systems When the Reproductive Processed Is Described by Integrals with Degenerate Kernels. Applied Mathematics (AM), 4, 1376-1380.
http://dx.doi.org/10.4236/am.2013.410186

[6]   Duduchava, R.V. (1973) Unidimensional Singular Integral Operator Algebras in Spaces of Holder Functions with Weight. Proceedings of A. Razmadze Mathematical Institute, 43, 19-52. (In Russian)

 
 
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