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Complex Approximations, Orthogonal Polynomials and Applications (CAOPA)
April 11, 2022 20:00–21:00, Moscow, online via Zoom at 17:00 GMT (=13:00 EDT=18:00 BST=19:00 CEST=20:00 Msk)
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Spectral properties of some tridiagonal matrices
A. V. Dyachenko Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow
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Abstract:
In the talk, we survey a few recent works on spectral properties of
tridiagonal matrices — including certain our results. In particular, we
compare several viewpoints to generalised Sylvester–Kac matrices, as
well as to other matrices whose spectra are “linear” (i.e., spectral
points constitute arithmetic progressions). In connection with this
question, we present a nice property tridiagonal matrices with zero
diagonals, give some examples of Leonard pairs and a certain related
algebraic structure. We also briefly touch upon matrices whose spectra
are simple and “quadratic”.
The talk is based on a joint work with Mikhail Tyaglov.
Language: English
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