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Soliton Equations and their Algebro-Geometric Solutions
As a partner to Volume 1: Dimensional Continuous Models, this monograph provides a self-contained introduction to algebro-geometric solutions of completely integrable, nonlinear, partialExpand
On spectral theory for Schrödinger operators with strongly singular potentials
We examine two kinds of spectral theoretic situations: First, we recall the case of self-adjoint half-line Schrodinger operators on [a , ∞), a ∈ ℝ, with a regular finite end point a and the case ofExpand
A new approach to inverse spectral theory, II. General real potentials and the connection to the spectral measure
We continue the study of the A-amplitude associated to a half-line Schrodinger operator, - d^2/dx^2 + q in L^2((0,b)), b ≤ ∞ A is related to the Weyl-Titchmarsh m-function via m(-k^2) = -k- ʃ^a_0Expand
Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum
We discuss results where the discrete spectrum (or partial information on the discrete spectrum) and partial information on the potential q of a one-dimensional Schrodinger operator H =Expand
On Matrix–Valued Herglotz Functions
We provide a comprehensive analysis of matrix–valued Herglotz functions and illustrate their applications in the spectral theory of self–adjoint Hamiltonian systems including matrix–valuedExpand
m-Functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices
We study inverse spectral analysis for finite and semi-infinite Jacobi matricesH. Our results include a new proof of the central result of the inverse theory (that the spectral measure determinesH).Expand
Picard potentials and Hill's equation on a torus
Hill's equation has drawn an enormous amount of consideration due to its ubiquity in applications as well as its structural richness. Of particular importance in the last 20 years is its connectionExpand
Weyl-Titchmarsh theory for CMV operators associated with orthogonal polynomials on the unit circle
We provide a detailed treatment of Weyl-Titchmarsh theory for half-lattice and full-lattice CMV operators and discuss their systems of orthonormal Laurent polynomials on the unit circle, spectralExpand