This book deals with boundary value problems for analytic functions with applications to singular integral equations. New and simpler proofs of certain classical results such as the Plemelj formula, the Privalov theorem and the Poincare-Bertrand formula are given. Nearly one third of this book contains the author's original works, most of which were not published in English and, hence, were previously unknown to most readers in the world. This book consists of seven chapters together with an appendix: chapter 1 describes the basic knowledge on Cauchy-type integrals and Cauchy principal value integrals, chapters II and III study respectively fundamental boundary value problems and their applications to singular integral equations for closed contours, chapters IV and V discuss the same problems for curves with nodes (including open arcs), chapter VI deals with similar problems for systems of functions, chapter VII is concerned with some miscellaneous problems and the Appendix contains some basic results on Fredholm integral equations. In most sections, there are carefully selected sets of exercises, some of which supplement the text of the sections; answers/hints are also given for some of those exercises.
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"The book is self-contained and clearly written ... It can well be used for advanced courses in complex analysis and for seminars, and is readable by graduate students themselves." Mathematics Abstracts
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Inside This Book
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First Sentence:
One of the most important tools in theory of boundary value problems for analytic functions is the Cauchy-type integral. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
extended residue theorem, sectionally holomorphic function, compound boundary value problems, regular solution system, involution formulas, partial indices, smooth closed contour, unique simple pole, canonical matrix, singular integral equations, interior region bounded, canonical function, definite branch, ordinary nodes, canonical matrices, congruent points, jump problem, oriented positively, generalized degree, jump curve, continuous branch, homogeneous problem, fractional linear transformations, present paragraph, automorphic function Key Phrases - Capitalized Phrases (CAPs): (learn more)
Exercise Prove New!
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Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
One of the most important tools in theory of boundary value problems for analytic functions is the Cauchy-type integral. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
extended residue theorem, sectionally holomorphic function, compound boundary value problems, regular solution system, involution formulas, partial indices, smooth closed contour, unique simple pole, canonical matrix, singular integral equations, interior region bounded, canonical function, definite branch, ordinary nodes, canonical matrices, congruent points, jump problem, oriented positively, generalized degree, jump curve, continuous branch, homogeneous problem, fractional linear transformations, present paragraph, automorphic function Key Phrases - Capitalized Phrases (CAPs): (learn more)
Exercise Prove New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Front Flap | Table of Contents | First Pages | Index | Back Flap | Back Cover | Surprise Me!
Citations (learn more)
This book cites 16
books:
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- Integral Equations (Wiley Classics Library) by Harry Hochstadt on page 337, Back Matter (1), and Back Matter (2)
- Introduction To Compact Lie Groups (Series in Pure Mathematics) by Howard D Fegan in Front Matter
- Geometry of Spherical Space Form Groups, (Series in Pure Mathematics) by Peter B. Gilkey in Front Matter
- Metric Rigidity Theorems on Hermitian Locally Symmetric Manifolds (Series in Pure Mathematics, V. 6) by Ngaiming Mok in Front Matter
- Class Number Parity (Series in Pure Mathematics) by P. E. Conner in Front Matter
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