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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Direct computation of the spectral function


Author: Amin Boumenir
Journal: Proc. Amer. Math. Soc. 123 (1995), 3431-3436
MSC: Primary 34B24; Secondary 34L05
MathSciNet review: 1283541
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Abstract: We would like to find an explicit formula for the spectral function of the following Sturm-Liouville problem:

$\displaystyle \left\{ {\begin{array}{*{20}{c}} {Lf \equiv - \frac{{{d^2}}}{{d{x... ...\quad x \geq 0,} \hfill \\ {f'(0) - mf(0) = 0.} \hfill \\ \end{array} } \right.$

A simple operational calculus argument will help us obtain an explicit formula for the transmutation kernel. The expression of the spectral function is then obtained through the nonlinear integral equation found in the Gelfand-Levitan theory.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1283541-5
PII: S 0002-9939(1995)1283541-5
Article copyright: © Copyright 1995 American Mathematical Society