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Factorization of Functional Operators with Involutive Rotation on the Unit Circle
Institute of Basic Sciences and Engineering, Hidalgo State University, Pachuca, Mexico
Institute of Basic Sciences and Engineering, Hidalgo State University, Pachuca, Mexico
- 1 Institute of Basic Sciences and Engineering, Hidalgo State University, Pachuca, Mexico
- 2 Institute of Basic Sciences and Engineering, Hidalgo State University, Pachuca, Mexico
Applied Mathematics·Volume 11 (2020)·Pages 1132–1138·Published 2 November 2020·DOI10.4236/am.2020.1111076
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Abstract
Following the classical definition of factorization of matrix-functions, we introduce a definition of factorization for functional operators with involutive rotation on the unit circle. Partial indices are defined and their uniqueness is proven. In previous works, the main research method for the study scalar singular integral operators and Riemann boundary value problems with Carlemann shift were operator identities, which allowed to eliminate shift and to reduce scalar problems to matrix problems without shift. In this study, the operator identities were used for the opposite purpose: to transform operators of multiplication by matrix-functions into scalar operators with Carlemann linear-fractional shift.
KeywordsCarlemann ShiftOperator IdentitiesFactorizationInvolutive Rotation
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