This book presents the main results and methods on inverse spectral problems for Sturm-
Liouville differential operators and their applications. Inverse problems of spectral analysis …

Continuation of Hermitian Positive Definite Functions and Related Questions Page 1 Integr. Equ.
Oper. Theory 78 (2014), 1–69 DOI 10.1007/s00020-013-2091-z Published online November …

The two-dimensional canonical system Jy′=− ℓ Hy where the nonnegative Hamiltonian
matrix function H (x) is trace-normed on (0,∞) has been studied in a function-theoretic way …

Motivated by the study of certain nonlinear wave equations (in particular, the Camassa–
Holm equation), we introduce a new class of generalized indefinite strings associated with …

We study spectral properties of two-dimensional canonical systems y′(t)= z JH (t) y (t), t∈[a,
b), where the Hamiltonian H is locally integrable on [a, b), positive semidefinite, and Weyl's …

We give a dynamical characterization of measures on the real line with finite logarithmic
integral. The general case is considered in the setting of evolution groups generated by de …

This largely self-contained treatment surveys, unites and extends some 20 years of research
on direct and inverse problems for canonical systems of integral and differential equations …

We characterize even measures μ= wd x+ μ s on the real line R with finite entropy integral∫
R log⁡ w (t) 1+ t 2 dt>−∞ in terms of 2× 2 Hamiltonians generated by μ in the sense of the …

Let the function Q be holomorphic in he upper half plane ℂ+ and such that Im Q (z≥ 0 and
Im zQ (z)≥ 0 if z ε ℂ+. A basic result of MG Krein states that these functions Q are the …

Based on continuity properties of the de Branges correspondence, we develop a new
approach to study the high-energy behavior of Weyl–Titchmarsh and spectral functions of 2× …