Ansaloni, Susanna
(2007)
On the spectrum of a parameter-dependent Sturm-Liouville problem.
[Preprint]
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Abstract
We study the spectrum of a parameter dependent Sturm-Liouville problem by using the continued fractions, through which necessary and sufficient conditions for eigenvalues are obtained. From these conditions estimates for large eigenvalues depending on the parameter and an asymptotic result for the lowest eigenvalue will follow. Furthermore, the use of the theory of orthogonal polynomials provides upper and lower bounds for the eigenvalues given in terms of the zeros of particular sequences of polynomials.
Abstract
We study the spectrum of a parameter dependent Sturm-Liouville problem by using the continued fractions, through which necessary and sufficient conditions for eigenvalues are obtained. From these conditions estimates for large eigenvalues depending on the parameter and an asymptotic result for the lowest eigenvalue will follow. Furthermore, the use of the theory of orthogonal polynomials provides upper and lower bounds for the eigenvalues given in terms of the zeros of particular sequences of polynomials.
Document type
Preprint
Creators
Keywords
Sturm-Liouville problem, semiclassical limit, clustering
Subjects
DOI
Deposit date
18 May 2007
Last modified
16 May 2011 12:06
URI
Other metadata
Document type
Preprint
Creators
Keywords
Sturm-Liouville problem, semiclassical limit, clustering
Subjects
DOI
Deposit date
18 May 2007
Last modified
16 May 2011 12:06
URI
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