On Factorization of Functional Operators with Reflection on the Real Axis
| Autor: | Anna Tarasenko, Oleksandr Karelin |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
General Mathematics
010102 general mathematics Multiplicative function Singular integral 01 natural sciences 010305 fluids & plasmas Matrix decomposition Algebra Matrix (mathematics) Riemann hypothesis symbols.namesake Reflection (mathematics) Factorization Matrix function 0103 physical sciences symbols 0101 mathematics Mathematics |
| Zdroj: | WSEAS TRANSACTIONS ON MATHEMATICS. 20:171-177 |
| ISSN: | 2224-2880 1109-2769 |
| DOI: | 10.37394/23206.2021.20.18 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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