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Published online by Cambridge University Press: 23 December 2009
Proof is the idol before whom the pure mathematician tortures himself.
Sir Arthur EddingtonIn this appendix we indicate the role of Herglotz functions(cf. Appendix I) in connection with spectral theory of Schrödinger operators on the half-line [0, ∞) and on all of ℝ. The material presented includes a discussion of (matrix-valued) spectral functions and asymptotic spectral parameter expansions of half-line Weyl–Titchmarsh m-functions for general (i.e., not necessarily Dirichlet) boundary conditions. We also treat the special case of algebro-geometric potentials and explicitly compute the corresponding spectral matrix.
We start with Schrödinger operators on the half-line [0, ∞) under the following basic assumptions.
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