Cauchy Type Singular Integral Equations.

      Аннотация: This work introduces the Cauchy type singular integral equations and it's connection with boundary value problems for analytic functions. It investigates briefly but profoundly this subject which is scattered in the literature. Special emphasis is given to the technique of solving certain classes of equations of this type and to the theory of Riemann-Hilbert boundary value problems and it's role in invsetigating and solving singular integral equations of the Cauchy type. A brief review of the literature on this subject is also given.

Ключевые слова: Analytic functions, Integral equations, Paths, regions, singular, Cauchy, Improper integral, Fredholm Integral Equation, Abel's Equation, Closed Contour, Open Contour, Riemann Boundary value problem, Hilbert Boundary value problem, simply connected domain, Cauchy Type of the first kind, Cauchy Type of the second kind, Beta function, Principle value of the integral