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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Boundary conditions in the infinite interval and some related results.


Author: Rao V. Govindaraju
Journal: Trans. Amer. Math. Soc. 154 (1971), 113-128
MSC: Primary 34.30
DOI: https://doi.org/10.1090/S0002-9947-1971-0269912-2
MathSciNet review: 0269912
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Abstract: The number of square-integrable solutions of a real, selfadjoint differential equation are determined using exclusively the elementary theory of matrices. Boundary conditions in the infinite interval are given a simple format and a relation between any two selfadjoint boundary conditions is deduced. Finally a lemma due to Titchmarsh, which forms the basis of eigenfunction expansions, is generalized.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0269912-2
Keywords: Selfadjoint differential operators, selfadjoint boundary conditions, fundamental set of solutions, eigenvalues, symplectic matrices, Everitt surfaces, circles in matrix space
Article copyright: © Copyright 1971 American Mathematical Society