7,206 research outputs found
The Two-Spectra Inverse Problem for Semi-Infinite Jacobi Matrices in The Limit-Circle Case
We present a technique for reconstructing a semi-infinite Jacobi operator in
the limit circle case from the spectra of two different self-adjoint
extensions. Moreover, we give necessary and sufficient conditions for two real
sequences to be the spectra of two different self-adjoint extensions of a
Jacobi operator in the limit circle case.Comment: 26 pages. Changes in the presentation of some result
From Random Matrices to Quasiperiodic Jacobi Matrices via Orthogonal Polynomials
We present an informal review of results on asymptotics of orthogonal
polynomials, stressing their spectral aspects and similarity in two cases
considered. They are polynomials orthonormal on a finite union of disjoint
intervals with respect to the Szego weight and polynomials orthonormal on R
with respect to varying weights and having the same union of intervals as the
set of oscillations of asymptotics. In both cases we construct double infinite
Jacobi matrices with generically quasiperiodic coefficients and show that each
of them is an isospectral deformation of another. Related results on asymptotic
eigenvalue distribution of a class of random matrices of large size are also
shortly discussed
Inverse problems for Jacobi operators II: Mass perturbations of semi-infinite mass-spring systems
We consider an inverse spectral problem for infinite linear mass-spring
systems with different configurations obtained by changing the first mass. We
give results on the reconstruction of the system from the spectra of two
configurations. Necessary and sufficient conditions for two real sequences to
be the spectra of two modified systems are provided.Comment: 25 pages, 2 figures. Typos were corrected, two remarks were added,
material added to Sec.
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