Continuity and compactness of singular integral operators

In the space of square integrable functions we establish effective sufficient continuity and compactness conditions for singular integral operators with Cauchy kernels on a segment of the real axis.     

Finite-dimensional approximations of singular integrals and direct methods of solution of singular integral and integrodifferential equations

A brief survey is given of papers reviewed in RZh Matematika in the last 15 years (1965–1979) on applied methods of calculating various classes of one-dimensional and multidimensional singular integrals and quadrature methods of solving various classes of singular linear equations with integrals in the sense of principal values.Translated from Itogi Nauki i Tekhniki, Seriya Matematicheskii Analiz, Vol. 18, pp. 251–307, 1980.     

Methods for solving a singular integral equation with Cauchy kernel on the real line

We study exact and approximate methods for solving a singular integral equation with Cauchy kernel on the real line. On the basis of the theory of positive operators, we prove an existence and uniqueness theorem for this equation in the space of Lebesgue square integrable functions. This theorem is then used to give a theoretical justification of general projection and projection-iteration methods as well as an iteration method for solving this equation.     

Solid-State Decarboxylation of Cyclophane Tetra(malonatemethylene) Derivative

Russian Journal of General Chemistry - Heat-induced solid-state decarboxylation of tetra(malonatemethylene) based cyclophane leads to its tetra(2-carboxyethyl) derivative in quantitative yield....