Author: Mordukha'i Moiseevich Va'inberg
Publisher:
ISBN:
Category : Banach spaces
Languages : en
Pages : 323

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Author: Mordukhaĭ Moiseevich Vaĭnberg
Publisher:
ISBN:
Category : Nonlinear theories
Languages : en
Pages :

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Book Description

Author: Mordukhaǐ Moiseevich Vaǐnberg
Publisher:
ISBN:
Category : Nonlinear theories
Languages : en
Pages : 323

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Book Description

Author: L. Nirenberg
Publisher: American Mathematical Soc.
ISBN: 0821828193
Category : Mathematics
Languages : en
Pages : 159

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Book Description
Since its first appearance as a set of lecture notes published by the Courant Institute in 1974, this book served as an introduction to various subjects in nonlinear functional analysis. The current edition is a reprint of these notes, with added bibliographic references. Topological and analytic methods are developed for treating nonlinear ordinary and partial differential equations. The first two chapters of the book introduce the notion of topological degree and develop its basic properties. These properties are used in later chapters in the discussion of bifurcation theory (the possible branching of solutions as parameters vary), including the proof of Rabinowitz global bifurcation theorem. Stability of the branches is also studied. The book concludes with a presentation of some generalized implicit function theorems of Nash-Moser type with applications to Kolmogorov-Arnold-Moser theory and to conjugacy problems. For more than 20 years, this book continues to be an excellent graduate level textbook and a useful supplementary course text. Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.

Author: Anthony Francis Ruston
Publisher: Cambridge University Press
ISBN: 9780521604932
Category : Mathematics
Languages : en
Pages : 314

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Book Description
Presents analogues for operators on Banach spaces of Fredholm's solution of integral equations of the second kind.

Author: R. M. Dudley
Publisher: Springer
ISBN: 3540488146
Category : Mathematics
Languages : en
Pages : 289

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Book Description
The book is about differentiability of six operators on functions or pairs of functions: composition (f of g), integration (of f dg), multiplication and convolution of two functions, both varying, and the product integral and inverse operators for one function. The operators are differentiable with respect to p-variation norms with optimal remainder bounds. Thus the functions as arguments of the operators can be nonsmooth, possibly discontinuous, but four of the six operators turn out to be analytic (holomorphic) for some p-variation norms. The reader will need to know basic real analysis, including Riemann and Lebesgue integration. The book is intended for analysts, statisticians and probabilists. Analysts and statisticians have each studied the differentiability of some of the operators from different viewpoints, and this volume seeks to unify and expand their results.

Author: Harbir Antil
Publisher: Springer
ISBN: 1493986368
Category : Mathematics
Languages : en
Pages : 434

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Book Description
This volume provides a broad and uniform introduction of PDE-constrained optimization as well as to document a number of interesting and challenging applications. Many science and engineering applications necessitate the solution of optimization problems constrained by physical laws that are described by systems of partial differential equations (PDEs)​. As a result, PDE-constrained optimization problems arise in a variety of disciplines including geophysics, earth and climate science, material science, chemical and mechanical engineering, medical imaging and physics. This volume is divided into two parts. The first part provides a comprehensive treatment of PDE-constrained optimization including discussions of problems constrained by PDEs with uncertain inputs and problems constrained by variational inequalities. Special emphasis is placed on algorithm development and numerical computation. In addition, a comprehensive treatment of inverse problems arising in the oil and gas industry is provided. The second part of this volume focuses on the application of PDE-constrained optimization, including problems in optimal control, optimal design, and inverse problems, among other topics.

Author: Mordukhaĭ Moiseevich Vaĭnberg
Publisher:
ISBN:
Category : Mathematical analysis
Languages : en
Pages : 346

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"The subject to which this book is devoted should be of interest both to pure mathematicians and to workers in applied sciences who are increaslingly often required to deal with nonlinear systems and their associated nonlinear equations. The main subject has up to the present time appeared only in Russian journals. As the author's techniques are directed mainly towards proving existence theorems (largely concerning nonlinear integral operators), rather than developing techniques for the actual solution of nonlinear equations, it was thought the addition of the last chapter of the Russian book "Functional analysis in normed spaces" by L.V. Kantorovich and G.P. Akilov devoted to the extension of Newton's method to nonlinear functional equations would substantially increase the usefulness of this translation"--Translator's preface.

Author: Jozef T. Devreese
Publisher: Springer Science & Business Media
ISBN: 1468428209
Category : Science
Languages : en
Pages : 379

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Book Description
The Advanced Study Institute on 'Elementary Excitations in Solids, Molecules, and Atoms' was held at the University of Antwerp (U.I.A.) from June 18th till June 30th 1973. The In stitute was sponsored by NATO. Co-sponsors were: Agfa-Gevaert N.V. (Mortsel - Belgium), Bell Telephone Mfg. Co. (Antwerp Belgium), the National Science Foundation (Washington D.C. - U.S.A.) and the University of Antwerp (U.I.A.). A total of 120 lecturers and participants attended the Institute. Over the last few years, substantial progress has been made in the description of the elementary excitations of the elec tronic and vibrational systems and their interactions. Parallel with this, the experimentalists have obtained outstanding re sults, partly as a result of availability of coherent light sour ces from the far infrared through the visible region, and partly because of the availability of synchrotron radiation sources in the soft X-ray region. The results of today will lead to fur ther progress over the next years. It was the purpose of this NATO Advanced Study Institute to present astate of the art, namely a survey of experiment and theory.

Author: Vladimir I. Bogachev
Publisher: Springer Nature
ISBN: 3030382192
Category : Mathematics
Languages : en
Pages : 586

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Book Description
This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.