Riemann boundary problem with infinite index of logarithmic order on a spiral-form contour. I

We study the Riemann boundary problem with infinite index of logarithmic order on an open rectifiable Jordan spiral-form contour, here the influence of the contour on the solvability of the problem is comparable with the influence of the argument of its coefficient. An explicit solution of the problem is constructured in the class of functions admitting weak-power singularities at the ends of a line of conjugacy.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 11, pp. 1509–1517, November, 1990.