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Karelin, A.A. (2001) On a Relation between Singular Integral Operators with a Carlemann Linear-Fractional Shift and Matrix Characteristic Operators without Shift. Boletín de la Sociedad Matemátlca Mexicana, 7, 235-246.

has been cited by the following article:

• TITLE: Factorization of Functional Operators with Involutive Rotation on the Unit Circle

  AUTHORS: Aleksandr Karelin, Anna Tarasenko

  KEYWORDS: Carlemann Shift, Operator Identities, Factorization, Involutive Rotation

  JOURNAL NAME: Applied Mathematics, Vol.11 No.11, November 16, 2020

  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.