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AuthorMuskhelishvili, N. I. author
TitleSingular Integral Equations [electronic resource] : Boundary problems of functions theory and their applications to mathematical physics / by N. I. Muskhelishvili
ImprintDordrecht : Springer Netherlands, 1958
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Descript 447p. online resource


In preparing this translation for publication certain minor modifications and additions have been introduced into the original Russian text, in order to increase its readibility and usefulness. Thus, instead of the first person, the third person has been used throughout; wherever possible footnotes have been included with the main text. The chapters and their subsections of the Russian edition have been renamed parts and chapters respectively and the last have been numbered consecutively. An authors and subject index has been added. In particular, the former has been combined with the list of references of the original text, in order to enable the reader to find quickly all information on anyone reference in which he may be especially interested. This has been considered most important with a view to the difficulties experienced outside Russia in obtaining references, published in that country. Russian names have been printed in Russian letters in the authors index, in order to overcome any possible confusion arising from transliteration


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

Mathematics Integral equations Mechanics Mathematics Integral Equations Mechanics


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