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" Carleman's Formulas in Complex Analysis : "
by Lev Aizenberg.
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BL
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| Record Number
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774881
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b594876
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| Main Entry
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by Lev Aizenberg.
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| Title & Author
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Carleman's Formulas in Complex Analysis : : Theory and Applications\ by Lev Aizenberg.
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| Publication Statement
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Dordrecht : Springer Netherlands, 1993
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| Series Statement
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Mathematics and Its Applications, 244.
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| Page. NO
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(xx, 299 pages)
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| ISBN
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9401115966
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: 9789401115964
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| Contents
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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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| Abstract
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This monograph is the first to give 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 the latest results, including those obtained by computer simulation on the elimination of noise in a given frequency band. For mathematicians and theoretical physicists whose work involves complex analysis, and those interested in signal processing.
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| Subject
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Functions of complex variables.
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Mathematics.
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Physical Sciences Mathematics.
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| LC Classification
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QA331.B954 1993
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| Added Entry
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L A Aĭzenberg
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