On the Spectral Expansions Connected with Schrödinger’s Operator of Continuous Functions in a Closed Domain
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Keywords

Eigenfunction, Eigenvalues, Expansions, Regularization, Riesz means, Mean value formula, Singular potential, Boundary problem, Hamiltonian, Sobolev spaces.

How to Cite

Abdumalik A. Rakhimov, Kamran Zakaria, & Nazir Ali Khan. (2012). On the Spectral Expansions Connected with Schrödinger’s Operator of Continuous Functions in a Closed Domain. Journal of Basic & Applied Sciences, 8(2), 613–617. https://doi.org/10.6000/1927-5129.2012.08.02.56

Abstract

Present paper is devoted to study of uniformly convergence of spectral expansions in a closed domain. We consider here as a spectral expansions eigenfunction expansions connected with one Schrodinger’s operator with singular potential in two dimensional domains with smooth boundary.

https://doi.org/10.6000/1927-5129.2012.08.02.56
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References

Reed M., Simon B., Methods of Modern Mathematical Physics, I. Functional Analsis, New York London 1972; p. 357.

Il’in V.?., Spectral theory of differential operators. Moscow. «Nauka», 1991, p. 367.

Reed M., Simon B, Methods of Modern Mathematical Physics, II. Fourier Analysis, Self-adjoiness, Academic Press New York London, 1978; p. 394.

Rakhimov A.A., Kamran Zakariya. On an Estimation of Eigenfunctions of Schrödinger’s Operatorin a Closed Domain, MathDigest, UPM, Malaysia, June edition, 2010; p. 1-4.

Alimov Sh. A., Il'in V. A., Nikishin E.M., Convergence problems of multiple trigonometric series and spectral decompositions. I, Uspekhi Mat. Nauk, 1976; 31: 28-83.

Rakhimov A. A. On the uniformly convergence spectral expansions of continuous functions in a closed domain. J. Izvestiya of Uzbek Academy of Science, 1987; 6: 17-22.

Alimov Sh. A., Rakhimov A.A. On the localization spectral expansions in a closed domain, J. Differential Equations 1997; 33: 80-2.

Alimov Sh. A., Rakhimov A.A.: On uniformly convergence of spectral expansions in a closed domain, Doclades of Uzbek Acad Science, 1986; 10: 5-7.

Khalmukhamedov A.R. Spectral theory of elliptic equations with singular coefficients, Doctoral Thesis, Tashkent, 1998, p. 1-205.

Moiseev E.I. The uniform convergence of certain expansions in a closed domain, Soviet Math Dokl 1977; 18: 549-53.