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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
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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

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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