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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