Kovalyova G. Theory of solvability and approximate solution of singular integral equations and their systems in non-normal case

The object is singular integral equations with Cauchy kernel and their systems with symbol vanishing on infinite set of zero measure on the contour. The aims are developing of theory of solvability and establishing of methods for approximate solution. The methods are methods of theory of singular integral equations, methods of complex analysis, methods of common theory of approximate methods. Theoretical results and novelty - normalizing spaces for full singular integral equations with Cauchy kernel and their systems and for some classes of singular integral equations with Carleman shift and conjugation was constructed under assumption of special factorability of their symbols; sufficient conditions for convergence of reduction and collocation methods for approximate solution of singular integral equations and their systems in non-normal case on unit circle was established; algorithm for counting of number and found of linear independent solutions of homogeneous systems of singular integral equationswith orientation-reversing Carleman shift was proposed. Sphere of use is theory of singular integral equations, theory of elasticity, aerodynamics and hydrodynamics.