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On two-dimensional singular integral operators with conformal Carleman shift
For the class of singular integral operators with continuous coefficients and with the conformal shift over a two-dimensional bounded domain an explicit Fredholm property criterion is obtained. Operators under consideration have kernels either with positive or with negative ; the conformal shift , is of Carleman type: for k = 1, 2, ..., n Γ’β¬β 1 and W^n = I. It is proved also that a Fredholm operator A of such type has trivial index Ind A =