Author | Muskhelishvili, N. I. author |
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Title | Singular Integral Equations [electronic resource] : Boundary problems of functions theory and their applications to mathematical physics / by N. I. Muskhelishvili |
Imprint | Dordrecht : Springer Netherlands, 1958 |
Connect to | http://dx.doi.org/10.1007/978-94-009-9994-7 |
Descript | 447p. online resource |
I Fundamental Propkrtibs of Cauchy Integrals -- 1 The Holder Condition -- 2 Integrals of the Cauehy type -- 3 Some corollaries on Cauehy integrals -- 4 Cauehy integrals near ends of the line of integration -- II The Hilbert and the Biemann-Helbert Problems and Singular Integral Equations (Case of Contours) -- 5 The Hilbert and Riemann-Hilbert boundary problems -- 6 Singular integral equations with Cauehy type kernels (case of contours) -- III Applications to Some Boundary Problems -- 7 The Dirichlet problem -- 8 Various representations of holomorpkic functions by Cauehy and analogous integrals -- 9 Solution of the generalized Riemann-Hilbert-Poincarรฉ problem -- IV The Hilbert Problem in the Case of Arcs or Discontinuous Boundary Conditions and Some of its Applications -- 10 The Hilbert problem in the case of arcs or discontinuous boundary conditions -- 11 Inversion formulae for arcs -- 12 Effective solution of some boundary problems of the theory of harmonic functions -- 13 Effective solution of the principal problems of the static theory of elasticity for the half-plane, circle and analogous regions -- V Singular Integral Equations for the Case of Arcs or Discontinuous Coefficients and Some of their Applications -- 14 Singular integral equations for the case of arcs and continuous coefficients -- 15 Singular integral equations in the case of discontinuous coefficients -- 16 Application to the Dirichlet problem and similar problems -- 17 Solution of the intgro-differential-equation of the theory of aircraft wings of finite span -- VI The Hilbert Problem for Several Unknown Functions and Systems of Singular Integral Equations -- 18 The Hilbert problem for several unknown functions -- 19 Systems of singular integral equations with Cauchy type kernels and some supplements -- Appendix 1 On smooth and piecewise smooth lines -- Appendix 2 On the behaviour of the Cauchy integral near corner points -- Appendix 3 An elementary proposition regarding bi-orthogpnal systems of functions -- References and author index