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Green's Functions for Singular Ordinary Differential Operators

Published online by Cambridge University Press:  20 November 2018

Fred Brauer
Fred Brauer*
Affiliation:
University of Wisconsin and Massachusetts Institute of Technology
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There are several ways to approach the eigenfunction expansion problem for ordinary differential operators via the spectral theorem for self-ad joint linear operators in Hilbert space. One can examine the resolvent, which requires a detailed study of the Green's function (4, 5, 7), or one can use the spectral theorem for unbounded operators (2, 3, 9). Since the eigenf unction expansion theorem also requires some multiplicity theory, unless one is prepared to use a rather powerful form of the spectral theorem for unbounded operators, as in (2, 9), the proof requires a good deal of work in addition to the spectral theorem.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 571 - 582
Copyright
Copyright © Canadian Mathematical Society 1967

References

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