A brilliant monograph, directed to graduate and advanced-undergraduate students, on the theory of boundary value problems for analytic functions and its applications to the solution of singular integral equations with Cauchy and Hilbert kernels. With exercises.
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Text: English (translation)
Original Language: Russian
Original Language: Russian
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4 of 5 people found the following review helpful:
5.0 out of 5 stars
Remarkable text on advanced complex analysis.,
This review is from: Boundary Value Problems (Paperback)
This book should be the natural continuation of regular complex analysis courses. It presents the full theory of the Cauchy integral and applies it to solve important problems on differential and integral equations, potential theory, etc.Its contents are: Integrals of the Cauchy type, the Riemann boundary value problem, singular integral equations with Cauchy kernel, the Hilbert boundary value problem and singular integral equations with Hilbert kernel, various generalized boundary value problems, boundary value problems and singular integral equations with discontinuous coefficients and open contours, integral equations soluble in closed form. Includes motivation and full explanations for each topic, excercises and historical notes for each chapter, and extensive references. The way the author chose his material (most of it researched by himself) makes this text the perfect connection between complex analysis and the other topics I told before, and also constitutes the path to follow if one is interested in hypercomplex analysis. Please read the rest of my reviews (just click on my name above).
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