Acta Mathematica Vietnamica
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ON SINGULAR INTEGRAL EQUATIONS WITH THE CARLEMAN SHIFTS IN THE CASE OF THE VANISHING COEFFICIENT
LE HUY CHUAN, NGUYEN MINH TUANpp. 319-333
Abstract
Based on the well-known necessary and sufficient condition for the linear-fractional function to be the generator of a cyclic group of $n$-terms, this paper describes the general form of all linear-fractional functions which are Carleman shifts on the unit circle. Our main result deals with the solvability in a closed form for a class of singular integral equations with Carleman shifts on the unit circle in the case where the coefficient vanishes on the curve.