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Factorisation of triangular matrix-functions of arbitrary order

Presented by: 
Sergei Rogosin
Tuesday 13th August 2019 - 13:30 to 14:30
INI Seminar Room 1
It will be discussed an efficient method for factorization of square triangular matrix-functions of arbitrary order which was recently proposed in [1]. The idea goes back to the paper by G. N. Chebotarev [2] who constructed factorisation of 2x2 triangular matrix-functions by using representation of the certain functions related to entries of the initial matrix into continuous fraction. In order to avoid additional technical difficulties, we consider matrix-functions with Hoelder continuous entries. Tough the proposed method could be realised for wider classes of matrix-functions. Chebotarev's method is extended here to the triangular matrix-functions of arbitrary order. An inductive consideration which allows to obtain such an extension is based on an auxiliary statement.
Theoretical construction is illustrated by a number of examples.
The talk is based on a joint work with Dr. L. Primachuk and Dr. M.Dubatovskaya.

1. Primachuk, L., Rogosin, S.: Factorization of triangular matrix-functions of an arbitrary order, Lobachevsky J. Math., 39 (6), 809–817 (2018)
2. Chebotarev, G. N.: Partial indices of the Riemann boundary value problem with a triangular matrix of the second order, Uspekhi Mat. Nauk, XI (3(69)), 192_202 (1956) (in Russian).
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons