APPROXIMATE METHODS FOR SINGULAR INTEGRAL EQUATIONS WITH A NON-CARLEMAN SHIFT

It is known that some problems of synthesis with continuous time and stationary parameters can be reduced to the solution of Wiener-Hopf equations on the semiaxis R+ = [0, ∞). If the problem of synthesis is not stationary, then the Wiener-Hopf method is not applicable. In this case the problem of synthesis is reduced to a singular integral equation Tφ = f on the unit circle T with a non-Carleman shift of T onto itself, which has a finite set of fixed points. An estimate for dim ker T is obtained and an approximation algorithm of this estimate is given. For the case dim ker T = 0 we construct an approximate solution of the equation Tφ = f.