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4 Limiting Values of the Cauchy Type Integral Integrals over
The Hilbert Formulae for the Limiting Values of the Real
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adjoint arbitrary constants assume automorphic function boundary condition boundary value problem bounded canonical function Cauchy kernel Cauchy type integral class of functions closed contour conditions of solubility conformal mapping Consequently considered curve deduced defined denote density derivatives determined Dirichlet problem domain D+ dominant equation Fredholm equation Fredholm integral equation Fredholm kernel function analytic function F(z Hence Hilbert boundary value Hilbert problem Holder condition homogeneous equation homogeneous problem I. N. Vekua ib(s insoluble integral representation investigation limiting values linearly independent linearly independent solutions method multiply-connected domain non-homogeneous problem number of solutions obtain open contour plane pole polynomial prove reduced regularizator regularizing factor relation Riemann boundary value Riemann problem right-hand side satisfies the condition satisfies the Holder Schwarz operator sectionally analytic function single-valued singular equation singular integral equation Sokhotski formulae solution of equation solving theorem theory unit circle unknown function vanish zero