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5.—Separation of Variables (An Abstract Approach)

Published online by Cambridge University Press:  14 February 2012

Synopsis

For a certain class of operators in the direct product of two Hilbert spaces, two problems are solved: the inhomogeneous operator equation, and the eigenvalue problem. Illustrative examples are given.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1974

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References

References to Literature

[1] Akhiezer, N. I. and Glazman, I. M., 1961. Theory of Linear Operators in Hilbert Space, 1. New York: Ungar. (Translated from the Russian by Nestell, M..)Google Scholar
[2] Apostol, T. M., 1971. Mathematical Analysis. London: Addison-Wesley.Google Scholar
[3] Dieudonné, J., 1969. Foundations of Modern Analysis. New York: Academic Press.Google Scholar
[4] Dunford, N. and Schwartz, J. T., 1964. Linear Operators, part 1, General Theory. New York: Interscience.Google Scholar
[5] Friedman, B., 1956. An abstract formulation of the method of separation of variables. Proc. Conf. Differential Equations, University of Maryland, College Park, Md., 209226.Google Scholar
[6] Hille, E., 1959. Analytic Function Theory, 1. London: Ginn.Google Scholar
[7] Mohammed, S. A., 1972. Separation of Variables: An Abstract Approach. M.Sc. Dissertation, Dundee University.Google Scholar
[8] Murray, F. J. and Von Neumann, J., 1936. On rings of operators. Ann. Math., 37, 116229.CrossRefGoogle Scholar
[9] Stone, M. H., 1932. Linear transformations in Hilbert Space and their applications to analysis. Colloquium Publs Amer. Math. Soc., 15.CrossRefGoogle Scholar
[10] Taylor, A. E., 1958. Introduction to Functional Analysis. New York: Wiley.Google Scholar