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An example of spectral phase transition phenomenon in a class of Jacobi matrices with periodically modulated weights
Sergey Simonov
We consider self-adjoint unbounded Jacobi matrices with diagonal q_n=n and weights λ_n=c_n n, where c_n is a 2-periodical sequence of real numbers. The parameter space is decompose…
Spectral analysis of a class of hermitian Jacobi matrices in a critical (double root) hyperbolic case
Serguei Naboko, Sergey Simonov
We consider a class of Jacobi matrices with periodically modulated diagonal in a critical hyperbolic ("double root") situation. For the model with "non-smooth" matrix entries we ob…
Weyl-Titchmarsh functions of vector-valued Sturm-Liouville operators on the unit interval
Dmitry Chelkak, Evgeny Korotyaev
The matrix-valued Weyl-Titchmarsh functions of vector-valued Sturm-Liouville operators on the unit interval with the Dirichlet boundary conditions are considered. The collec…
Inverse resonance scattering for Jacobi operators
Evgeny Korotyaev
We consider the Jacobi operator on with a real compactly supported sequences and . We give the so…
The abstract Titchmarsh-Weyl M-function for adjoint operator pairs and its relation to the spectrum
Malcolm Brown, James Hinchcliffe, Marco Marletta +2
In the setting of adjoint pairs of operators we consider the question: to what extent does the Weyl M-function see the same singularities as the resolvent of a certain restriction…
Estimates for periodic Zakharov-Shabat operators
Evgeny Korotyaev, Pavel Kargaev
We consider the periodic Zakharov-Shabat operators on the real line. The spectrum of this operator consists of intervals separated by gaps with the lengths . L…