Geodesic
On the index of operators with end symbol
Izvestiya. Mathematics , Tome 63 (1999) no. 4, pp. 791-825.

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A study was made in [1] of the class of one-dimensional singular integral-functional equations closely connected with elliptic boundary-value problems on the plane in domains with piecewise-smooth boundaries. A criterion for the Fredholm property of these operators was formulated there in terms of the so-called end symbol. This symbol is a semi-almost periodic matrix-valued function assigned to the equation under consideration. In this paper we study this situation from a more general point of view. 
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A. P. Soldatov. On the index of operators with end symbol. Izvestiya. Mathematics , Tome 63 (1999) no. 4, pp. 791-825. http://geodesic.mathdoc.fr/item/IM2_1999_63_4_a7/

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