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Applications of multiparameter spectral theory to special functions

Published online by Cambridge University Press:  24 October 2008

Patrick J. Browne
Affiliation:
University of Calgary, Alberta T2N 1N4, Canada
B. D. Sleeman
Affiliation:
University of Dundee, Dundee DD1 HN4

Abstract

A recently discovered abstract relation arising in multiparameter spectral theory is used to unify some of the integral relations and equations associated with the ellipsoidal wave equation.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1980

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References

REFERENCES

(1)Arscott, F. M.Integral equations for ellipsoidal wave functions. Quart. J. Math. (Oxford) (2) 8 (1975) 223235.CrossRefGoogle Scholar
(2)Arscott, F. M.Periodic Differential Equations (London, Pergamon Press, 1964).Google Scholar
(3)Arscott, F. M.TWO parameter eigenvalue problems in differential equations. Proc. London Math. Soc. 14 (1964), 459470.CrossRefGoogle Scholar
(4)Atkinson, F. V.Multiparameter eigenvalue problems: matrices and compact operators (New York, Academic Press, 1972).Google Scholar
(5)Malurkar, S. L.Ellipsoidal wave functions. Indian J. of Phys. 9 (1935), 4580.Google Scholar
(6)Möglich, F.Beugunserscheinunger an Körpen von ellipsoidischer Gestalt. Ann. Physik 83 (1927), 609734.CrossRefGoogle Scholar
(7)Sleeman, B. D.Integral equations and relations for Lamé functions and ellipsoidal wave functions. Proc. Cambridge Philos. Soc. 64 (1968), 113126.CrossRefGoogle Scholar
(8)Sleeman, B. D. Multiparameter eigenvalue problems and k-linear operators. Proc. Conf. Theory of Ordinary and partial differential equations. Lecture Notes in Mathematics, no. 280 (1972), pp. 347353. Springer-Verlag.CrossRefGoogle Scholar
(9)Sleeman, B. D.Multiparameter spectral theory in Hilbert space (London, Pitman Press, 1978).CrossRefGoogle Scholar