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Large eigenvalues of a Sturm-Liouville problem

Published online by Cambridge University Press:  24 October 2008

J. H. E. Cohn
J. H. E. Cohn
Affiliation:
Bedford College, London
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Extract

Consider the eigenvalue problem

where q(x) is a (bounded) function in the class L(a, b). We may suppose without loss of generality that 0 ≤ α < π and 0 ≤ β < π. Then as is well known there are infinitely many eigenvalues λr (r = 0, 1, 2, …) and λn ∽ n2π2 (b − a)−2 as n → ∞.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 2 , April 1967 , pp. 473 - 475
Copyright
Copyright © Cambridge Philosophical Society 1967

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