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6 papers · 2 filters
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…
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…
M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems
B. M. Brown, G. Grubb, I. G. Wood
In this paper, we combine results on extensions of operators with recent results on the relation between the M-function and the spectrum, to examine the spectral behaviour of bound…
Borg type uniqueness Theorems for periodic Jacobi operators with matrix valued coefficients
Evgeny Korotyaev, Anton Kutsenko
We give a simple proof of Borg type uniqueness Theorems for periodic Jacobi operators with matrix valued coefficients.
Fourier transform, null variety, and Laplacian's eigenvalues
Rafael Benguria, Michael Levitin, Leonid Parnovski
We consider a quantity -- the distance to the origin from the null variety of the Fourier transform of the characteristic function of . We conjecture, firstly, that $κ(Ω)…