We have considered writing the present book for a long time, since the lack of a sufficiently complete textbook about complex analysis in infinite dimensional spaces was apparent. There are, however, some separate topics on this subject covered in the mathematical literature. For instance, the elementary theory of holomorphic vector functions.and mappings on Banach spaces is presented in the monographs of E. Hille and R. Phillips [1] and L. Schwartz [1], whereas some results on Banach algebras of holomorphic functions and holomorphic operator-functions are discussed in the books of W. Rudin [1] and T. Kato [1]. Apparently, the need to study holomorphic mappings in infinite dimensional spaces arose for the first time in connection with the development of nonlinear anal ysis. A systematic study of integral equations with an analytic nonlinear part was started at the end ofthe 19th and the beginning ofthe 20th centuries by A. Liapunov, E. Schmidt, A. Nekrasov and others. Their research work was directed towards the theory of nonlinear waves and used mainly the undetermined coefficients and the majorant power series methods. The most complete presentation of these methods comes from N. Nazarov. In the forties and fifties the interest in Liapunov's and Schmidt's analytic methods diminished temporarily due to the appearence of variational calculus meth ods (M. Golomb, A. Hammerstein and others) and also to the rapid development of the mapping degree theory (J. Leray, J. Schauder, G. Birkhoff, O. Kellog and others).
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0: Preliminaries.- I: Differential calculus in normed spaces.- II: Integration in normed spaces.- III: Holomorphic (analytic) operators and vector-functions on complex Banach spaces.- Capter IV: Linear operators.- V: Nonlinear equations with differentiable operators.- VI: Nonlinear equations with holomorphic operators.- VII: Banach manifolds.- VIII: Non-regular solutions of nonlinear equations.- IX: Operators on spaces with indefinite metric.- References.- List of Symbols.
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Hardcover. Condizione: new. Hardcover. The need to study holomorphic mappings in infinite dimensional spaces, in all likelihood, arose for the first time in connection with the development of nonlinear analysis. A systematic study of integral equations with an analytic nonlinear part was started at the end of the 19th and the beginning of the 20th centuries by A. Liapunov, E. Schmidt, A. Nekrasov and others. Their research work was directed towards the theory of nonlinear waves and used mainly the undetermined coefficients and the majorant power series methods, which subsequently have been refined and developed. Parallel with these achievements, the theory of functions of one or several complex variables was gradually enriched with more significant and subtle results. The present book is a first step towards establishing a bridge between nonlinear analysis, nonlinear operator equations and the theory of holomorphic mappings on Banach spaces. The work concludes with a brief exposition of the theory of spaces with indefinite metrics, and some relevant applications of the holomorphic mappings theory in this setting.In order to make this book accessible not only to specialists but also to students and engineers, the authors give a complete account of definitions and proofs, and also present relevant prerequisites from functional analysis and topology. Bridges the gap between nonlinear analysis, nonlinear operator equations and the theory of holomorphic mappings on Banach spaces. This book concludes with a brief exposition of the theory of spaces with indefinite metrics, and some relevant applications of the holomorphic mappings theory in this setting. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9783764329297
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Condizione: New. Bridges the gap between nonlinear analysis, nonlinear operator equations and the theory of holomorphic mappings on Banach spaces. This book concludes with a brief exposition of the theory of spaces with indefinite metrics, and some relevant applications of the holomorphic mappings theory in this setting. Series: Operator Theory: Advances and Applications. Num Pages: 294 pages, biography. BIC Classification: PBKD; PBKF; PBKJ; PDE; TBJ. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 234 x 156 x 17. Weight in Grams: 597. . 1993. Hardback. . . . . Codice articolo V9783764329297
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Gebunden. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 0: Preliminaries.- I: Differential calculus in normed spaces.- II: Integration in normed spaces.- III: Holomorphic (analytic) operators and vector-functions on complex Banach spaces.- Capter IV: Linear operators.- V: Nonlinear equations with differentiable . Codice articolo 5279018
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