Two inverse spectral problems for a class of singular Krein strings

We solve the inverse problem from the spectral measure and the inverse three-spectra problem for the class of singular Krein strings on a finite interval with trace class resolvents. In particular, this includes a complete description of all possible spectral measures and three (Dirichlet) spectra associated with this class of Krein strings. The solutions of these inverse problems are obtained by approximation with Stieltjes strings.Comment: 16 page

The inverse spectral transform for the conservative Camassa-Holm flow with decaying initial data

We establish the inverse spectral transform for the conservative Camassa-Holm flow with decaying initial data. In particular, it is employed to prove existence of weak solutions for the corresponding Cauchy problem.Comment: 27 page

Correlations and fluctuations of matrix elements and cross sections

The fluctuations and correlations of matrix elements of cross sections are investigated in open systems that are chaotic in the classical limit. The form of the correlation functions is discussed within a statistical analysis and tested in calculations for a damped quantum kicked rotator. We briefly comment on the modifications expected for systems with slowly decaying correlations, a typical feature in mixed phase spaces.Comment: 7 pages, 7 figure

On the connection between the Hilger and Radon--Nikodym derivatives

We show that the Hilger derivative on time scales is a special case of the Radon--Nikodym derivative with respect to the natural measure associated with every time scale. Moreover, we show that the concept of delta absolute continuity agrees with the one from measure theory in this context.Comment: 7 page