A new approach to inverse spectral theory. II: General real potentials and the connection to the spectral measure

Fritz Gesztesy and Barry Simon

Review from Zentralblatt MATH:

As in the previous paper by the second author [same journal 150, No. 3, 1029-1057 (1999; Zbl 0945.34013)] the authors consider the $A$-amplitude and the Weyl-Titchmarsh $m$-function for the radial Schrödinger equation on a finite interval or on the half line with a real-valued locally integrable potential. The asymptotic relation between $A$ and $m$ is investigated in more detail, a relation between $A$ and the spectral measure is obtained, a Laplace transform representation for $m$ is given, $m$-functions associated with other boundary conditions are discussed, and some examples are provided where $A$ can be computed exactly.

Reviewed by Tuncay Aktosun

Keywords: inverse spectral theory; Weyl-Titchmarsh $m$-function; spectral measure; radial Schrödinger equation

Classification (MSC2000): 34-99

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