Elements of the Theory of Functions and Functional Analysis: Metric and normed spaces. v. 2. Measure. The Lebesgue integral. Hilbert space
Author: Andreĭ Nikolaevich Kolmogorov
Publisher:
Published: 1963
Total Pages: 148
ISBN-13:
DOWNLOAD EBOOK →Lanterna Rally
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Real and Functional Analysis
Author: Vladimir I. Bogachev
Publisher: Springer Nature
Published: 2020-02-25
Total Pages: 586
ISBN-13: 3030382192
DOWNLOAD EBOOK →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.
Elements of the Theory of Functions and Functional Analysis
Author: Andreĭ Nikolaevich Kolmogorov
Publisher: Courier Corporation
Published: 1957
Total Pages: 166
ISBN-13: 9789998063754
DOWNLOAD EBOOK →Elements of the Theory of Functions and Functional Analysis
Author: Andreĭ Nikolaevich Kolmogorov
Publisher:
Published: 1957
Total Pages: 152
ISBN-13:
DOWNLOAD EBOOK →Fredholm Theory in Banach Spaces
Author: Anthony Francis Ruston
Publisher: Cambridge University Press
Published: 2004-06-03
Total Pages: 314
ISBN-13: 9780521604932
DOWNLOAD EBOOK →Presents analogues for operators on Banach spaces of Fredholm's solution of integral equations of the second kind.
Differentiable Measures and the Malliavin Calculus
Author: Vladimir Igorevich Bogachev
Publisher: American Mathematical Soc.
Published: 2010-07-21
Total Pages: 506
ISBN-13: 082184993X
DOWNLOAD EBOOK →This book provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure. In the infinite dimensional case new phenomena arise. For the first time a detailed account is given of the theory of differentiable measures, initiated by S. V. Fomin in the 1960s; since then the method has found many various important applications. Differentiable properties are described for diverse concrete classes of measures arising in applications, for example, Gaussian, convex, stable, Gibbsian, and for distributions of random processes. Sobolev classes for measures on finite and infinite dimensional spaces are discussed in detail. Finally, we present the main ideas and results of the Malliavin calculus--a powerful method to study smoothness properties of the distributions of nonlinear functionals on infinite dimensional spaces with measures. The target readership includes mathematicians and physicists whose research is related to measures on infinite dimensional spaces, distributions of random processes, and differential equations in infinite dimensional spaces. The book includes an extensive bibliography on the subject.
Measure Theory
Author: Vladimir I. Bogachev
Publisher: Springer Science & Business Media
Published: 2007-01-15
Total Pages: 1075
ISBN-13: 3540345140
DOWNLOAD EBOOK →This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.
Pareto-Nash-Stackelberg Game and Control Theory
Author: Valeriu Ungureanu
Publisher: Springer
Published: 2018-03-09
Total Pages: 343
ISBN-13: 3319751514
DOWNLOAD EBOOK →This book presents a comprehensive new, multi-objective and integrative view on traditional game and control theories. Consisting of 15 chapters, it is divided into three parts covering noncooperative games; mixtures of simultaneous and sequential multi-objective games; and multi-agent control of Pareto-Nash-Stackelberg-type games respectively. Can multicriteria optimization, game theory and optimal control be integrated into a unique theory? Are there mathematical models and solution concepts that could constitute the basis of a new paradigm? Is there a common approach and method to solve emerging problems? The book addresses these and other related questions and problems to create the foundation for the Pareto-Nash-Stackelberg Game and Control Theory. It considers a series of simultaneous/Nash and sequential/Stackelberg games, single-criterion and multicriteria/Pareto games, combining Nash and Stackelberg game concepts and Pareto optimization, as well as a range of notions related to system control. In addition, it considers the problems of finding and representing the entire set of solutions. Intended for researches, professors, specialists, and students in the areas of game theory, operational research, applied mathematics, economics, computer science and engineering, it also serves as a textbook for various courses in these fields.
Measure, Integration, and Functional Analysis
Author: Robert B. Ash
Publisher: Academic Press
Published: 2014-05-10
Total Pages: 301
ISBN-13: 1483265102
DOWNLOAD EBOOK →Measure, Integration, and Functional Analysis deals with the mathematical concepts of measure, integration, and functional analysis. The fundamentals of measure and integration theory are discussed, along with the interplay between measure theory and topology. Comprised of four chapters, this book begins with an overview of the basic concepts of the theory of measure and integration as a prelude to the study of probability, harmonic analysis, linear space theory, and other areas of mathematics. The reader is then introduced to a variety of applications of the basic integration theory developed in the previous chapter, with particular reference to the Radon-Nikodym theorem. The third chapter is devoted to functional analysis, with emphasis on various structures that can be defined on vector spaces. The final chapter considers the connection between measure theory and topology and looks at a result that is a companion to the monotone class theorem, together with the Daniell integral and measures on topological spaces. The book concludes with an assessment of measures on uncountably infinite product spaces and the weak convergence of measures. This book is intended for mathematics majors, most likely seniors or beginning graduate students, and students of engineering and physics who use measure theory or functional analysis in their work.
Metrics, Norms and Integrals
Author: J J Koliha
Publisher: World Scientific Publishing Company
Published: 2008-11-11
Total Pages: 428
ISBN-13: 9813101180
DOWNLOAD EBOOK →Metrics, Norms and Integrals is a textbook on contemporary analysis based on the author's lectures given at the University of Melbourne for over two decades. It covers three main topics: metric and topological spaces, functional analysis, and the theory of the Lebesgue integral on measure spaces. This self-contained text contains a number of original presentations, including an early introduction of pseudometric spaces to motivate general topologies, an innovative introduction to the Lebesgue integral, and a discussion on the use of the Newton integral. It is thus a valuable book to inform and stimulate both undergraduate and graduate students.
