On Invertibility of Functional Operators with Shift in Weighted Hölder Spaces

Anna Tarasenko^1*, Oleksandr Karelin²

¹Mathematical Research Center, Hidalgo State University, Pachuca, Mexico.
²Advanced Research Center on Industrial Engineering, Hidalgo State University, Pachuca, Mexico.

DOI: 10.4236/apm.2014.411068                

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

Conflicts of Interest

The authors declare no conflicts of interest.

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)