WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 20, 2021
On Factorization of Functional Operators with Reflection on the Real Axis
Authors: ,
Abstract: Problems of factorization of matrix functions are closely connected with the solution of matrix
Riemann boundary value problems and with the solution of vector singular integral equations. In this article, we
study functional operators with orientation-reversing shift reflection on the real axes. We introduce the concept
of multiplicative representation of functional operators with shift and its partial indices. Based on the classical
notion of matrix factorization, the correctness of the definitions is shown. A theorem on the relationship between
factorization of functional operators with reflection and factorization of the corresponding matrix functions is
proven.
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Keywords: Factorization, Functional operators, Carleman shift, Reflection, Matrix Riemann boundary value
Problem, Partial indices, Operator identities
Pages: 171-177
DOI: 10.37394/23206.2021.20.18