An important part of the theory of partial differential equations is the theory of boundary problems for elliptic equations and systems of equations. Among such problems those of greatest interest are the so-called non-Fredholm boundary prob- lems, whose investigation reduces, as a rule, to the study of singular integral equa- tions, where the Fredholm alternative is violated for these problems. Thanks to de- velopments in the theory of one-dimensional singular integral equations 28, 29], boundary problems for elliptic equations with two independent variables have been completely studied at...