An Introductory Course in Lebesgue Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introductory Course in Lebesgue Spaces write by Rene Erlin Castillo. This book was released on 2016-06-23. An Introductory Course in Lebesgue Spaces available in PDF, EPUB and Kindle. This book is devoted exclusively to Lebesgue spaces and their direct derived spaces. Unique in its sole dedication, this book explores Lebesgue spaces, distribution functions and nonincreasing rearrangement. Moreover, it also deals with weak, Lorentz and the more recent variable exponent and grand Lebesgue spaces with considerable detail to the proofs. The book also touches on basic harmonic analysis in the aforementioned spaces. An appendix is given at the end of the book giving it a self-contained character. This work is ideal for teachers, graduate students and researchers.
Fundamentals of Measurable Dynamics
Fundamentals of Measurable Dynamics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fundamentals of Measurable Dynamics write by Daniel J. Rudolph. This book was released on 1990. Fundamentals of Measurable Dynamics available in PDF, EPUB and Kindle. This book is designed to provide graduate students and other researchers in dynamical systems theory with an introduction to the ergodic theory of Lebesgue spaces. The author's aim is to present a technically complete account which offers an in-depth understanding of the techniques of the field, both classical and modern. Thus, the basic structure theorems of Lebesgue spaces are given in detail as well as complete accounts of the ergodic theory of a single transformation, ergodic theorems, mixing properties and entropy. Subsequent chapters extend the earlier material to the areas of joinings and representation theorems, in particular the theorems of Ornstein and Krieger. Prerequisites are a working knowledge of Lebesgue measure and the topology of the real line as might be gained from the first year of a graduate course. Many exercises and examples are included to illustrate and to further cement the reader's understanding of the material. The result is a text which will furnish the reader with a sound technical background from the foundations of the subject to some of its most recent developments.
An Introduction to Lebesgue Integration and Fourier Series
An Introduction to Lebesgue Integration and Fourier Series - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Lebesgue Integration and Fourier Series write by Howard J. Wilcox. This book was released on 2012-04-30. An Introduction to Lebesgue Integration and Fourier Series available in PDF, EPUB and Kindle. This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects. The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire. Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.
Variable Lebesgue Spaces
Variable Lebesgue Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Variable Lebesgue Spaces write by David V. Cruz-Uribe. This book was released on 2013-02-12. Variable Lebesgue Spaces available in PDF, EPUB and Kindle. This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, and for their applications to problems in physics and image processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-on approach that makes clear the similarities and differences between the variable and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewood maximal operator is completely developed, and the connections between variable Lebesgue spaces and the weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Riesz potentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolation from the theory of weighted norm inequalities. The final chapter applies the results from previous chapters to prove basic results about variable Sobolev spaces.
A First Course in Functional Analysis
A First Course in Functional Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A First Course in Functional Analysis write by Orr Moshe Shalit. This book was released on 2017-03-16. A First Course in Functional Analysis available in PDF, EPUB and Kindle. Written as a textbook, A First Course in Functional Analysis is an introduction to basic functional analysis and operator theory, with an emphasis on Hilbert space methods. The aim of this book is to introduce the basic notions of functional analysis and operator theory without requiring the student to have taken a course in measure theory as a prerequisite. It is written and structured the way a course would be designed, with an emphasis on clarity and logical development alongside real applications in analysis. The background required for a student taking this course is minimal; basic linear algebra, calculus up to Riemann integration, and some acquaintance with topological and metric spaces.
