Abstract.
In this paper we establish the connection between singular integral operators with conjugation and matrix functions consimilar to the identity. We show that any matrix function consimilar to the identity is factorable (in some space L p ) if and only if it admits a special factorization, that we call antisymmetric, and that this antisymmetric factorization has a direct connection with the factorization of singular integral operators with conjugation.
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Dedicated to the memory of Professor Georgii Litvinchuk
This research was supported by Centro de Análise Funcional e Aplicações (CEAF), IST – TULisbon, which is financed by FCT (Portugal).
Submitted: April 27, 2007. Accepted: January 23, 2008.
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Kravchenko, V.G., Lebre, A.B. & Rodríguez, J.S. Matrix Functions Consimilar to the Identity and Singular Integral Operators. Complex anal.oper. theory 2, 593–615 (2008). https://doi.org/10.1007/s11785-008-0068-8
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DOI: https://doi.org/10.1007/s11785-008-0068-8