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

A.A. BATUREV, V.G. KRAVCHENKO AND G.S. LITVINCHUK

Abstract:

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 semi-axis tex2html_wrap_inline13 . 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 tex2html_wrap_inline15 on the unit circle with a non-Carleman shift of onto itself, which has a finite set of fixed points. An estimate for tex2html_wrap_inline21 is obtained and an approximation algorithm of this estimate is given. For the case tex2html_wrap_inline23 we construct an approximate solution of the equation tex2html_wrap_inline15 .