Nilpotent Structures in Ergodic Theory - 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 Nilpotent Structures in Ergodic Theory write by Bernard Host. This book was released on 2018-12-12. Nilpotent Structures in Ergodic Theory available in PDF, EPUB and Kindle. Nilsystems play a key role in the structure theory of measure preserving systems, arising as the natural objects that describe the behavior of multiple ergodic averages. This book is a comprehensive treatment of their role in ergodic theory, covering development of the abstract theory leading to the structural statements, applications of these results, and connections to other fields. Starting with a summary of the relevant dynamical background, the book methodically develops the theory of cubic structures that give rise to nilpotent groups and reviews results on nilsystems and their properties that are scattered throughout the literature. These basic ingredients lay the groundwork for the ergodic structure theorems, and the book includes numerous formulations of these deep results, along with detailed proofs. The structure theorems have many applications, both in ergodic theory and in related fields; the book develops the connections to topological dynamics, combinatorics, and number theory, including an overview of the role of nilsystems in each of these areas. The final section is devoted to applications of the structure theory, covering numerous convergence and recurrence results. The book is aimed at graduate students and researchers in ergodic theory, along with those who work in the related areas of arithmetic combinatorics, harmonic analysis, and number theory.
Ergodic Theory
Ergodic Theory - 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 Ergodic Theory write by Cesar E. Silva. This book was released on 2023-07-31. Ergodic Theory available in PDF, EPUB and Kindle. This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, covers recent developments in classical areas of ergodic theory, including the asymptotic properties of measurable dynamical systems, spectral theory, entropy, ergodic theorems, joinings, isomorphism theory, recurrence, nonsingular systems. It enlightens connections of ergodic theory with symbolic dynamics, topological dynamics, smooth dynamics, combinatorics, number theory, pressure and equilibrium states, fractal geometry, chaos. In addition, the new edition includes dynamical systems of probabilistic origin, ergodic aspects of Sarnak's conjecture, translation flows on translation surfaces, complexity and classification of measurable systems, operator approach to asymptotic properties, interplay with operator algebras
Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits
Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits - 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 Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits write by Pablo Candela. This book was released on 2023-07-31. Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits available in PDF, EPUB and Kindle. View the abstract.
Discrete Analogues in Harmonic Analysis
Discrete Analogues in Harmonic 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 Discrete Analogues in Harmonic Analysis write by Ben Krause. This book was released on 2023-01-19. Discrete Analogues in Harmonic Analysis available in PDF, EPUB and Kindle. This timely book explores certain modern topics and connections at the interface of harmonic analysis, ergodic theory, number theory, and additive combinatorics. The main ideas were pioneered by Bourgain and Stein, motivated by questions involving averages over polynomial sequences, but the subject has grown significantly over the last 30 years, through the work of many researchers, and has steadily become one of the most dynamic areas of modern harmonic analysis. The author has succeeded admirably in choosing and presenting a large number of ideas in a mostly self-contained and exciting monograph that reflects his interesting personal perspective and expertise into these topics. —Alexandru Ionescu, Princeton University Discrete harmonic analysis is a rapidly developing field of mathematics that fuses together classical Fourier analysis, probability theory, ergodic theory, analytic number theory, and additive combinatorics in new and interesting ways. While one can find good treatments of each of these individual ingredients from other sources, to my knowledge this is the first text that treats the subject of discrete harmonic analysis holistically. The presentation is highly accessible and suitable for students with an introductory graduate knowledge of analysis, with many of the basic techniques explained first in simple contexts and with informal intuitions before being applied to more complicated problems; it will be a useful resource for practitioners in this field of all levels. —Terence Tao, University of California, Los Angeles
Linear and Quasilinear Parabolic Systems: Sobolev Space Theory
Linear and Quasilinear Parabolic Systems: Sobolev Space Theory - 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 Linear and Quasilinear Parabolic Systems: Sobolev Space Theory write by David Hoff. This book was released on 2020-11-18. Linear and Quasilinear Parabolic Systems: Sobolev Space Theory available in PDF, EPUB and Kindle. This monograph presents a systematic theory of weak solutions in Hilbert-Sobolev spaces of initial-boundary value problems for parabolic systems of partial differential equations with general essential and natural boundary conditions and minimal hypotheses on coefficients. Applications to quasilinear systems are given, including local existence for large data, global existence near an attractor, the Leray and Hopf theorems for the Navier-Stokes equations and results concerning invariant regions. Supplementary material is provided, including a self-contained treatment of the calculus of Sobolev functions on the boundaries of Lipschitz domains and a thorough discussion of measurability considerations for elements of Bochner-Sobolev spaces. This book will be particularly useful both for researchers requiring accessible and broadly applicable formulations of standard results as well as for students preparing for research in applied analysis. Readers should be familiar with the basic facts of measure theory and functional analysis, including weak derivatives and Sobolev spaces. Prior work in partial differential equations is helpful but not required.
