Singular Integral Equations: Boundary Problems of Function Theory and Their Application to Mathematical PhysicsSingular integral equations play important roles in physics and theoretical mechanics, particularly in the areas of elasticity, aerodynamics, and unsteady aerofoil theory. They are highly effective in solving boundary problems occurring in the theory of functions of a complex variable, potential theory, the theory of elasticity, and the theory of fluid mechanics. This high-level treatment by a noted mathematician considers one-dimensional singular integral equations involving Cauchy principal values. Its coverage includes such topics as the Hölder condition, Hilbert and Riemann-Hilbert problems, the Dirichlet problem, inversion formulas for arcs, and many other areas. Intended for graduate students, applied and pure mathematicians, engineers, physicists, and researchers in a variety of scientific and industrial fields, this text is accessible to students acquainted with the basic theory of functions of a complex variable and the theory of Fredholm integral equations. |
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applied arbitrary constants arbitrary polynomial assumed boundary condition boundary problems boundary value bounded at infinity bounded function Cauchy integral class H class h(c1 coefficients considered const continuous functions corresponding defined degree at infinity degree not greater denoted determined different from zero Dirichlet problem easily seen equivalent fact finite number Fredholm equation Fredholm integral equation Fredholm operator function p(t fundamental solution given class given function H condition half-plane hence homogeneous equation homogeneous Hilbert problem homogeneous problem I. N. Vekua infinite region last section linear linearly independent solutions matrix method necessary and sufficient non-special ends number of linearly obtained obviously particular solution plane polynomial of degree proved real constant real function reduced Riemann-Hilbert problem right side satisfies the H sectionally holomorphic function singular equation singular integral equations tangent theorem theory tion unknown function vanishing at infinity vector