Carleman’s Formulas in Complex Analysis
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Home > Mathematics and Science Textbooks > Mathematics > Calculus and mathematical analysis > Complex analysis, complex variables > Carleman’s Formulas in Complex Analysis: Theory and Applications(244 Mathematics and Its Applications)
Carleman’s Formulas in Complex Analysis: Theory and Applications(244 Mathematics and Its Applications)

Carleman’s Formulas in Complex Analysis: Theory and Applications(244 Mathematics and Its Applications)


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About the Book

This monograph gives a systematic presentation of the Carleman formulas. These enable values of functions holomorphic to a domain to be recovered from their values over a part of the boundary of the domain. Various generalizations of these formulas are considered. Applications are considered to problems of analytic continuation in the theory of functions, and, in a broader context, to problems arising in theoretical and mathematical physics, and to the extrapolation and interpolation of signals having a finite Fourier spectrum. The volume also contains a review of recent results, including those obtained by computer simulation on the elimination of noise in a given frequency band. It is suitable for mathematicians and theoretical physicists whose work involves complex analysis, and those interested in signal processing.

Table of Contents:
I. Carleman Formulas in the Theory of Functions of One Complex Variable and their Generalizations.- I. One-Dimensional Carleman Formulas.- II. Generalization of One-Dimensional Carleman Formulas.- II. Carleman Formulas in Multidimensional Complex Analysis.- III. Integral Representations of Holomorphic Functions of Several Complex Variables and Logarithmic Residues.- IV. Multidimensional Analog of Carleman Formulas with Integration over Boundary Sets of Maximal Dimension.- V. Multidimensional Carleman Formulas for Sets of Smaller Dimension.- VI. Carleman Formulas in Homogeneous Domains.- III. First Applications.- VII. Applications in Complex Analysis.- VIII. Applications in Physics and Signal Processing.- IX. Computing Experiment.- IV. Supplement to the English Edition.- X. Criteria for Analytic Continuation. Harmonic Extension.- XI. Carleman Formulas and Related Problems.- Notes.- Index of Proper Names.- Index of Symbols.


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Product Details
  • ISBN-13: 9780792321217
  • Publisher: Kluwer Academic Publishers
  • Publisher Imprint: Kluwer Academic Publishers
  • Height: 235 mm
  • No of Pages: 299
  • Returnable: Y
  • Sub Title: Theory and Applications
  • ISBN-10: 0792321219
  • Publisher Date: 31 Jan 1993
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Series Title: 244 Mathematics and Its Applications
  • Width: 155 mm


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Carleman’s Formulas in Complex Analysis: Theory and Applications(244 Mathematics and Its Applications)
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