Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-05T16:02:51.502Z Has data issue: false hasContentIssue false
  • English
  • Français

Eigenfunction expansions associated with a two-parameter system of differential equations

Published online by Cambridge University Press:  14 November 2011

M. Faierman
M. Faierman
Affiliation:
Department of Mathematics, University of the Witwatersrand, Johannesburg, South Africa
Get access Rights & Permissions [Opens in a new window]

Synopsis

Techniques from the theory of partial differential equations are employed to prove the uniform convergence of the eigenfunction expansion associated with a two-parameter system of ordinary differential equations of the second order.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 81 , Issue 1-2 , 1978 , pp. 79 - 93
Copyright
Copyright © Royal Society of Edinburgh 1978

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Atkinson, F. V.Multiparameter eigenvalue problems, 1 (New York: Acadamic. 1972).Google Scholar
2Browne, P. J.A multi-parameter eigenvalue problem. J. Math. Anal. Appl. 38 (1972), 553–568.CrossRefGoogle Scholar
3Faierman, M. On the distribution of the eigenvalues of a two-parameter system of ordinary differential equations of the second order. Siam J. Math. Anal., to appear.Google Scholar
4Dixon, A. C.Harmonic expansions of functions of two variables. Proc. London Math. Soc. 5 (1907), 411–478.Google Scholar
5Hilbert, D.Grundzuge einer allgemeiner theorie der linearen Integralgleichungen (New York: Chelsea, 1953).Google Scholar
6Faierman, M.The expansion theorem in multiparameters Sturm-Liouville theory. Lecture Notes in Mathematics 415 (Berlin: Springer, 1974).Google Scholar
7Faierman, M.A note on the eigenfunction expansion associated with a multiparameter eigenvalue problem in ordinary differential equations. Ben Gurion Univ. Dept. Math. Report 137 (1976).Google Scholar
8Agmon, S.Lectures on elliptic boundary value problems (New York: Van Nostrand, 1965).Google Scholar
9Miranda, C.Partial differential equations of elliptic type, 2nd edn (Berlin: Springer, 1970).Google Scholar
10Lions, J. L. and Magenes, E.Non-homogeneous boundary value problems and applications, 1 (Berlin: Springer, 1972).Google Scholar
11Mizohata, S.The theory of partial differential equations (Cambridge: University Press, 1973).Google Scholar
12Faierman, M.An oscillation theorem for a one-parameter ordinary differential equation of the second order. J. Differential Equations 11 (1972), 10–37.Google Scholar
13Bers, L., John, F. and Schechter, M.Partial Differential Equations III (New York: Interscience, 1964).Google Scholar
14Riesz, F. and Sz.-Nagy, B.Functional Analysis (New York: Ungar, 1955).Google Scholar
15Titchmarsh, E. C.Eigenfunction expansions associated with second-order differential equations, I, 2nd edn (Oxford: Clarendon Press, 1962).Google Scholar
16Ladyzhenskaya, O. A. and Ural'tseva, N. N.Linear and quasilinear elliptic equations (New York: Academic, 1968).Google Scholar