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arXiv · 1101.2989

Continued fraction solution of Krein's inverse problem

Yves Tourigny
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Abstract

The spectral data of a vibrating string are encoded in its so-called characteristic function. We consider the problem of recovering the distribution of mass along the string from its characteristic function. It is well-known that Stieltjes' continued fraction provides a solution of this inverse problem in the particular case where the distribution of mass is purely discrete. We show how to adapt Stieltjes' method to solve the inverse problem for a related class of strings. An application to the excursion theory of diffusion processes is presented.

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Yves Tourigny. 2011-05-19. Continued fraction solution of Krein's inverse problem. https://doi.org/10.1088/0266-5611%2F27%2F8%2F085008

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