ON THE UNIFORMLY CONVERGENCE SPECTRAL EXPANSIONS CONNECTED WITH SCHRÖDINGER’S OPERATOR OF CONTINUOUS FUNCTIONS IN A CLOSED DOMAIN

Authors

  • A. A. Rakhimov Laboratory of Methods of Modern Mathematical Physics, Mathematical Sciences and Research Centre, Federal Urdu University, Karachi, Pakistan Department of Mathematics, NED University, Karachi, Pakistan
  • K. Zakaria Laboratory of Methods of Modern Mathematical Physics, Mathematical Sciences and Research Centre, Federal Urdu University, Karachi, Pakistan Department of Mathematics, NED University, Karachi, Pakistan
  • N. A. Khan Laboratory of Methods of Modern Mathematical Physics, Mathematical Sciences and Research Centre, Federal Urdu University, Karachi, Pakistan Department of Mathematics, NED University, Karachi, Pakistan

DOI:

https://doi.org/10.71330/thenucleus.2010.870

Abstract

Present paper is devoted to study summability problem 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

References

M. Reed and B. Simon, Methods of Modern

Mathematical Physics, I. Functional Analysis,

New York, London (1972) p.357.

E.B. Davies, Spectral theory and differential

operators, Cambridge University Press

(1995) p. 188.

M. Reed, B. Simon, Methods of Modern

Mathematical Physics, II. Fourier Analysis,

Self-adjoiness, Academic Press New York

London (1978) p.394.

Sh. A. Alimov, V.A. Il'in and E.M. Nikishin,

Convergence, Uspekhi Mat. Nauk, 31:6(192)

(1976) 28.

V.Ð. Il’in, Spectral Theory of Differential

Operators, Moscow, Nauka (1991) 367.

E.I. Moiseev, Soviet Math. Dokl 18 (1977)

A.A. Rakhimov, Z. Kamran, On an Estimation

of Eigenfunctions of Schrödinger’s Operatorin

a Closed Domain, MathDigest, UPM,

Malaysia, June Edition (2010) p. 23-27.

A.A. Rakhimov, J. Izvestiya of Uzbek

Academy of Science N 6 (1987) 17.

A.R. Khalmukhamedov, Spectral Theory of

Elliptic Equations with Singular Coefficients,

Doctoral Thesis, Tashkent (1998) p.1-205.

A.A. Rakhimov, J. Astrophysics and Applied

Mathematics V1 (2009) 100.

Downloads

Published

07-12-2010

How to Cite

[1]
A. A. Rakhimov, K. Zakaria, and N. A. Khan, “ON THE UNIFORMLY CONVERGENCE SPECTRAL EXPANSIONS CONNECTED WITH SCHRÖDINGER’S OPERATOR OF CONTINUOUS FUNCTIONS IN A CLOSED DOMAIN”, The Nucleus, vol. 47, no. 4, pp. 261–265, Dec. 2010.

Issue

Vol. 47 No. 4 (2010)

Section

Articles

License

For all articles published in The Nucleus, copyright is retained by the authors. Articles are licensed under an open access licence [CC Attribution 4.0] meaning that anyone may download and read the paper for free. In addition, the article may be reused and quoted provided that the original published version is cited properly.