integration and modern analysis birkhauser advanced texts basler lehrbucher

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Integration And Modern Analysis

Author : John J. Benedetto
ISBN : 0817646566
Genre : Mathematics
File Size : 67. 3 MB
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This textbook and treatise begins with classical real variables, develops the Lebesgue theory abstractly and for Euclidean space, and analyzes the structure of measures. The authors' vision of modern real analysis is seen in their fascinating historical commentary and perspectives with other fields. There are comprehensive treatments of the role of absolute continuity, the evolution of the Riesz representation theorem to Radon measures and distribution theory, weak convergence of measures and the Dieudonné–Grothendieck theorem, modern differentiation theory, fractals and self-similarity, rearrangements and maximal functions, and surface and Hausdorff measures. There are hundreds of illuminating exercises, and extensive, focused appendices on functional and Fourier analysis. The presentation is ideal for the classroom, self-study, or professional reference.

Integration A Functional Approach

Author : Klaus Bichteler
ISBN : 3764359366
Genre : Mathematics
File Size : 47. 6 MB
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This book covers Lebesgue integration and its generalizations from Daniell's point of view, modified by the use of seminorms. Integrating functions rather than measuring sets is posited as the main purpose of measure theory. From this point of view Lebesgue's integral can be had as a rather straightforward, even simplistic, extension of Riemann's integral; and its aims, definitions, and procedures can be motivated at an elementary level. The notion of measurability, for example, is suggested by Littlewood's observations rather than being conveyed authoritatively through definitions of (sigma)-algebras and good-cut-conditions, the latter of which are hard to justify and thus appear mysterious, even nettlesome, to the beginner. The approach taken provides the additional benefit of cutting the labor in half. The use of seminorms, ubiquitous in modern analysis, speeds things up even further. The book is intended for the reader who has some experience with proofs, a beginning graduate student for example. It might even be useful to the advanced mathematician who is confronted with situations - such as stochastic integration - where the set-measuring approach to integration does not work. ------ Reviews This book provides a complete and rapid introduction to Lebesgue integration and its generalizations from Daniell’s point of view, (...) The development is clear and it contains interesting historical notes and motivations, abundant exercises and many supplements. The connection with the historical development of integration theory is also pointed out. - Zentralblatt MATH The material is well motivated and the writing is pleasantly informal. (...) There are numerous exercises, many destined to be used later in the text, and 15 pages of solutions/hints. - Mathematical Reviews

Functional Analysis Harmonic Analysis And Image Processing A Collection Of Papers In Honor Of Bj Rn Jawerth

Author : Michael Cwikel
ISBN : 9781470428365
Genre : Fourier analysis
File Size : 52. 21 MB
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This volume is dedicated to the memory of Björn Jawerth. It contains original research contributions and surveys in several of the areas of mathematics to which Björn made important contributions. Those areas include harmonic analysis, image processing, and functional analysis, which are of course interrelated in many significant and productive ways. Among the contributors are some of the world's leading experts in these areas. With its combination of research papers and surveys, this book may become an important reference and research tool. This book should be of interest to advanced graduate students and professional researchers in the areas of functional analysis, harmonic analysis, image processing, and approximation theory. It combines articles presenting new research with insightful surveys written by foremost experts.

Numerical Analysis And Its Applications

Author : Ivan Dimov
ISBN : 9783319570990
Genre : Computers
File Size : 24. 74 MB
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This book constitutes thoroughly revised selected papers of the 6th International Conference on Numerical Analysis and Its Applications, NAA 2016, held in Lozenetz, Bulgaria, in June 2016. The 90 revised papers presented were carefully reviewed and selected from 98 submissions. The conference offers a wide range of the following topics: Numerical Modeling; Numerical Stochastics; Numerical Approx-imation and Computational Geometry; Numerical Linear Algebra and Numer-ical Solution of Transcendental Equations; Numerical Methods for Differential Equations; High Performance Scientific Computing; and also special topics such as Novel methods in computational finance based on the FP7 Marie Curie Action,Project Multi-ITN STRIKE - Novel Methods in Compu-tational Finance, Grant Agreement Number 304617; Advanced numerical and applied studies of fractional differential equations.

Measure Theory And Functional Analysis

Author : Nik Weaver
ISBN : 9789814508582
Genre : Mathematics
File Size : 46. 42 MB
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This book provides an introduction to measure theory and functional analysis suitable for a beginning graduate course, and is based on notes the author had developed over several years of teaching such a course. It is unique in placing special emphasis on the separable setting, which allows for a simultaneously more detailed and more elementary exposition, and for its rapid progression into advanced topics in the spectral theory of families of self-adjoint operators. The author's notion of measurable Hilbert bundles is used to give the spectral theorem a particularly elegant formulation not to be found in other textbooks on the subject. Request Inspection Copy

Real Analysis

Author : Emmanuele DiBenedetto
ISBN : 0817642315
Genre : Mathematics
File Size : 61. 14 MB
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The focus of this modern graduate text in real analysis is to prepare the potential researcher to a rigorous "way of thinking" in applied mathematics and partial differential equations. The book will provide excellent foundations and serve as a solid building block for research in analysis, PDEs, the calculus of variations, probability, and approximation theory. All the core topics of the subject are covered, from a basic introduction to functional analysis, to measure theory, integration and weak differentiation of functions, and in a presentation that is hands-on, with little or no unnecessary abstractions. Additional features: * Carefully chosen topics, some not touched upon elsewhere: fine properties of integrable functions as they arise in applied mathematics and PDEs – Radon measures, the Lebesgue Theorem for general Radon measures, the Besicovitch covering Theorem, the Rademacher Theorem; topics in Marcinkiewicz integrals, functions of bounded variation, Legendre transform and the characterization of compact subset of some metric function spaces and in particular of Lp spaces * Constructive presentation of the Stone-Weierstrass Theorem * More specialized chapters (8-10) cover topics often absent from classical introductiory texts in analysis: maximal functions and weak Lp spaces, the Calderón-Zygmund decomposition, functions of bounded mean oscillation, the Stein-Fefferman Theorem, the Marcinkiewicz Interpolation Theorem, potential theory, rearrangements, estimations of Riesz potentials including limiting cases * Provides a self-sufficient introduction to Sobolev Spaces, Morrey Spaces and Poincaré inequalities as the backbone of PDEs and as an essential environment to develop modern and current analysis * Comprehensive index This clear, user-friendly exposition of real analysis covers a great deal of territory in a concise fashion, with sufficient motivation and examples throughout. A number of excellent problems, as well as some remarkable features of the exercises, occur at the end of every chapter, which point to additional theorems and results. Stimulating open problems are proposed to engage students in the classroom or in a self-study setting.

An Introduction To Measure Theory

Author : Terence Tao
ISBN : 9780821869192
Genre : Mathematics
File Size : 73. 64 MB
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This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Caratheodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.

Measures Integrals And Martingales

Author : Ren L. Schilling
ISBN : 9781316620243
Genre : Mathematics
File Size : 77. 27 MB
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A concise, elementary introduction to measure and integration theory, requiring few prerequisites as theory is developed quickly and simply.

Elements Of Nonlinear Analysis

Author : Michel Chipot
ISBN : 3764364068
Genre : Mathematics
File Size : 60. 79 MB
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The goal of this book is to present some modern aspects of nonlinear analysis. Some of the material introduced is classical, some more exotic. We have tried to emphasize simple cases and ideas more than complicated refinements. Also, as far as possible, we present proofs that are not classical or not available in the usual literature. Of course, only a small part of nonlinear analysis is covered. Our hope is that the reader - with the help of these notes - can rapidly access the many different aspects of the field. We start by introducing two physical issues: elasticity and diffusion. The pre sentation here is original and self contained, and helps to motivate all the rest of the book. Then we turn to some theoretical material in analysis that will be needed throughout (Chapter 2). The next six chapters are devoted to various aspects of elliptic problems. Starting with the basics of the linear theory, we introduce a first type of nonlinear problem that has today invaded the whole mathematical world: variational inequalities. In particular, in Chapter 6, we introduce a simple theory of regularity for nonlocal variational inequalities. We also attack the question of the existence, uniqueness and approximation of solutions of quasilinear and mono tone problems (see Chapters 5, 7, 8). The material needed to read these parts is contained in Chapter 2. The arguments are explained using the simplest possible examples.

A Concrete Introduction To Higher Algebra

Author : Lindsay N. Childs
ISBN : 9780387745275
Genre : Mathematics
File Size : 35. 59 MB
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This book is an informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. The new examples and theory are built in a well-motivated fashion and made relevant by many applications - to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises are found throughout the book.

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