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The complex analysis, also known as theory of analytic functions or complex variable function theory, is the part of mathematical analysis that investigates the functions of complex numbers, their analyticity, holomorphicity, and integration of these functions on complex domains that can be complex manifolds or submanifolds. Also the extensions of these domains to the complex projective spaces and complex topological groups are study themes. The analytic continuing of complex domains where complex series representations are used and the exploring of singularities whose integration invariants obtain values as zeros of certain polynomials of the complex rings of certain vector bundles are important in the exploring of new function classes in the meromorphic context and also arithmetic context. Also important are established correspondences with complex vector spaces, or even in their real parts, using several techniques of complex geometrical analysis, Nevanlinna methods, and other techniques as the modular forms. All this is just some examples of great abundance of the problems in mathematics research that require the complex analysis application. This book covers some interesting and original research of certain topics of complex analysis. Also included are some applications for inverse and ill posed problems developed in engineering and applied research.

Analytic functions.

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Spectral theory and complex analysis

Functional analysis. --- Spectral theory (Mathematics) --- Analytic functions. --- Functional analysis --- Analytic functions --- Analyse fonctionnelle --- Spectre (Mathématiques) --- Fonctions analytiques --- ELSEVIER-B EPUB-LIV-FT --- Algèbres topologiques --- Fonctions de plusieurs variables complexes --- Operator theory --- Complex analysis

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Bernstein functions appear in various fields of mathematics, e.g. probability theory, potential theory, operator theory, functional analysis and complex analysis - often with different definitions and under different names. Among the synonyms are `Laplace exponent' instead of Bernstein function, and complete Bernstein functions are sometimes called `Pick functions', `Nevanlinna functions' or `operator monotone functions'. This monograph - now in its second revised and extended edition - offers a self-contained and unified approach to Bernstein functions and closely related function classes, bringing together old and establishing new connections. For the second edition the authors added a substantial amount of new material. As in the first edition Chapters 1 to 11 contain general material which should be accessible to non-specialists, while the later Chapters 12 to 15 are devoted to more specialized topics. An extensive list of complete Bernstein functions with their representations is provided.

Analytic functions. --- Monotonic functions. --- Quasianalytic functions. --- Functions, Quasianalytic --- Quasi-analytic functions --- Quasientire functions in the sense of Bernstein --- Analytic functions --- Functions, Monotonic --- Functions of real variables --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Functions of complex variables --- Series, Taylor's --- Bernstein Function. --- Monotone Function. --- Probability Measure. --- Semigroup. --- Theory.

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Presents an introduction to the properties of analytic functions. This title provides examples of functional equations to show how analytic solutions can be found. It treats analytic functions as those generated by sequences with positive radii of convergence.

Analytic functions. --- Functional equations. --- Power series. --- Series, Power --- Equations, Functional --- Functional analysis --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Functions of complex variables --- Series, Taylor's

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Bounded analytic functions

Mathematical analysis --- Analytic functions. --- Functional analysis. --- Functional analysis --- Analytic functions --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Functions of complex variables --- Series, Taylor's --- 517.53 --- 517.53 Functions of a complex variable --- Functions of a complex variable