A new approach to inverse spectral theory. II: General real potentials and the connection to the spectral measure (Q1840453)

As in the previous paper by the second author [ibid. 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. An 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.