Singular integral operators on complicated contours and pseudodifferential operators

We apply the pseudodifferential operator technique to the study of algebras of singular operators on complicated contours. This technique is used to construct a symbolic calculus for theC ^*-algebra generated by singular integral operators whose coefficients may have singularities of the second kind on complicated contours; the curves forming a node are not required to have a tangent at the node. Translated fromMatematicheskie Zametki, Vol. 58, No. 1, pp. 67–85, July, 1995. This work was partially supported by the Russian Foundation for Basic Research under grant No. 93-04-691.