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25.—On the Eigenfunction Expansion associated with a Singular Complex-valued Fourth-order Differential Equation*

Published online by Cambridge University Press:  14 February 2012

Jyoti Chaudhuri  and
V. Krishna Kumar
Jyoti Chaudhuri
Affiliation:
Department of Pure Mathematics, University of Calcutta
V. Krishna Kumar
Affiliation:
Department of Mathematics, University of Dundee
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Synopsis

The direct convergence theory of eigenfunction expansions associated with boundry value problems, not necessarily self-adjoint, generated from complex-valued fourth-order symmetric ordinary differential expressions on semi-infinite intervals, is discussed. An admissible class of functions for the expansion is characterised. Also a generalisation of Stieltjes representation theorem for analytic functions discussed in [13, §§ 22.23 and 24] is obtained.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 75 , Issue 4 , 1976 , pp. 325 - 332
Copyright
Copyright © Royal Society of Edinburgh 1976

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