Publication
Riemann–Hilbert problems, Toeplitz operators and Q-classes
| Summary: | We generalize the notion of Q-classes C(Q1,Q2) , which was introduced in the context of Wiener–Hopf factorization, by considering very general 2 × 2 matrix functions Q1, Q2. This allows us to use a mainly algebraic approach to obtain several equivalent representations for each class, to study the intersections of Q-classes and to explore their close connection with certain non-linear scalar equations. The results are applied to various factorization problems and to the study of Toeplitz operators with symbol in a Q-class. We conclude with a group theoretic interpretation of some of the main results. |
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| Main Authors: | Câmara, M. C. |
| Other Authors: | Malheiro, Teresa |
| Subject: | Riemann–Hilbert problems Toeplitz operators Factorization matrix equations Ciências Naturais::Matemáticas |
| Year: | 2014 |
| Country: | Portugal |
| Document type: | article |
| Access type: | open access |
| Associated institution: | Universidade do Minho |
| Language: | English |
| Origin: | RepositóriUM - Universidade do Minho |
| Summary: | We generalize the notion of Q-classes C(Q1,Q2) , which was introduced in the context of Wiener–Hopf factorization, by considering very general 2 × 2 matrix functions Q1, Q2. This allows us to use a mainly algebraic approach to obtain several equivalent representations for each class, to study the intersections of Q-classes and to explore their close connection with certain non-linear scalar equations. The results are applied to various factorization problems and to the study of Toeplitz operators with symbol in a Q-class. We conclude with a group theoretic interpretation of some of the main results. |
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