Abstract
The author investigates the piecewise-continuous Riemann boundary-value problem with index minus infinity on a closed rectifiable Jordan curve; the index of the problem is a measure of the integral effect exerted on the solvability of the problem by the argument and modulus of the coefficient, and also by the properties of the junction curve. Discontinuities of the second kind are admitted in the logarithm of the coefficient and in the free term. The solution of the problem is constructed explicitly in the class of functions having a weak power singularity.
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