Carleman's formulas in complex analysis : theory and applications

Preface. Foreword to the English Translation. Preliminaries. Part I: Carleman Formulas in the Theory of Functions of One Complex Variable and their Generalization. I. One-Dimensional Carleman Formulas. II. Generalizations of One-Dimensional Carleman Formulas. Part 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 the Boundary Sets of Maximal Dimension. V. Multidimensional Carleman Formulas for Sets of Smaller Dimension. VI. Carleman Formulas in Homogeneous Domains. Part III: First Applications. VII. Applications in Complex Analysis. VIII. Applications in Physics and Signal Processing. IX. Computing Experiment. Part IV: Supplement to English Edition. X. Criteria for Analytic Continuation Harmonic Extension. XI. Carleman Formulas and Related Problems. Bibliography. Notes. Index of Proper Names. Subject Index. Index of Symbols.

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