On a Banach Algebra Generated by the Bergman Operator, Constant Coefficients, and Finitely Generated Groups of Shifts
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We study a Banach algebra generated by the Bergman operator, constant coefficients, and shifts formed by finitely generated commutative groups of hyperbolic transformations of a unit disk acting in the Lebesgue space L p , p > 1, and obtain an efficient criterion for the operators from the considered Banach algebra to be Fredholm operators.
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- 2.A. B. Antonevich, Linear Functional Equations. Operator Approach [in Russian], Universitetskoe, Minsk (1988).Google Scholar
- 3.G. S. Litvinchuk, Boundary-Value Problems and Singular Integral Equations with Shift [in Russian], Nauka, Moscow (1977).Google Scholar
- 4.Y. I. Karlovich, “Local-trajectory method for the investigation of invertibility in C*-algebras of operators with discrete groups of shifts,” Dokl. Akad. Nauk SSSR, 299, No. 3, 546–550 (1988).Google Scholar
- 6.B. A. Plamenevskii, Algebras of Pseudodifferential Operators [in Russian], Nauka, Moscow (1986).Google Scholar
- 9.M. A. Naimark, Normed Rings [in Russian], Nauka, Moscow (1968).Google Scholar