Special Issue on Ergodic Theory and Harmonic Analysis
Author | : S. C. Bagchi |
Publisher | : |
Total Pages | : 440 |
Release | : 2000 |
Genre | : Ergodic theory |
ISBN | : |
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Author | : S. C. Bagchi |
Publisher | : |
Total Pages | : 440 |
Release | : 2000 |
Genre | : Ergodic theory |
ISBN | : |
Author | : Joseph Rosenblatt |
Publisher | : American Mathematical Soc. |
Total Pages | : 242 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 0821842358 |
There are strong connections between harmonic analysis and ergodic theory. A recent example of this interaction is the proof of the spectacular result by Terence Tao and Ben Green that the set of prime numbers contains arbitrarily long arithmetic progressions. This text presents a series of essays on the topic.
Author | : Karl Endel Petersen |
Publisher | : Cambridge University Press |
Total Pages | : 452 |
Release | : 1995 |
Genre | : Ergodic theory |
ISBN | : 0521459990 |
Tutorial survey papers on important areas of ergodic theory, with related research papers.
Author | : Karl Endel Petersen |
Publisher | : |
Total Pages | : 450 |
Release | : 2014-05-14 |
Genre | : MATHEMATICS |
ISBN | : 9781107362048 |
Ergodic theory is a field that is stimulating on its own, and also in its interactions with other branches of mathematics and science. In recent years, the interchanges with harmonic analysis have been especially noticeable and productive. This book contains survey papers describing the relationship of ergodic theory with convergence, rigidity theory and the theory of joinings. These papers present the background of each area of interaction, the most outstanding results and promising lines of research. They should form perfect starting points for anyone beginning research in one of these areas. Thirteen related research papers describe the work; several treat questions arising from the Furstenberg multiple recurrence theory, while the remainder deal with convergence and a variety of other topics in dynamics.
Author | : Tanja Eisner |
Publisher | : Springer |
Total Pages | : 630 |
Release | : 2015-11-18 |
Genre | : Mathematics |
ISBN | : 3319168983 |
Stunning recent results by Host–Kra, Green–Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a modern foundation for introductory courses on ergodic theory, especially for students or researchers with an interest in functional analysis. While basic analytic notions and results are reviewed in several appendices, more advanced operator theoretic topics are developed in detail, even beyond their immediate connection with ergodic theory. As a consequence, the book is also suitable for advanced or special-topic courses on functional analysis with applications to ergodic theory. Topics include: • an intuitive introduction to ergodic theory • an introduction to the basic notions, constructions, and standard examples of topological dynamical systems • Koopman operators, Banach lattices, lattice and algebra homomorphisms, and the Gelfand–Naimark theorem • measure-preserving dynamical systems • von Neumann’s Mean Ergodic Theorem and Birkhoff’s Pointwise Ergodic Theorem • strongly and weakly mixing systems • an examination of notions of isomorphism for measure-preserving systems • Markov operators, and the related concept of a factor of a measure preserving system • compact groups and semigroups, and a powerful tool in their study, the Jacobs–de Leeuw–Glicksberg decomposition • an introduction to the spectral theory of dynamical systems, the theorems of Furstenberg and Weiss on multiple recurrence, and applications of dynamical systems to combinatorics (theorems of van der Waerden, Gallai,and Hindman, Furstenberg’s Correspondence Principle, theorems of Roth and Furstenberg–Sárközy) Beyond its use in the classroom, Operator Theoretic Aspects of Ergodic Theory can serve as a valuable foundation for doing research at the intersection of ergodic theory and operator theory
Author | : Karl E. Petersen |
Publisher | : Cambridge University Press |
Total Pages | : 0 |
Release | : 1995-01-27 |
Genre | : Mathematics |
ISBN | : 9780521459990 |
This volume contains articles that describe the connections between ergodic theory and convergence, rigidity theory, and the theory of joinings. These papers present the background of each area of interaction, the most outstanding recent results, and the currently promising lines of research. In the aggregate, they will provide a perfect introduction for anyone beginning research in one of these areas.
Author | : Karl E. Petersen |
Publisher | : |
Total Pages | : 448 |
Release | : 1995 |
Genre | : Electronic books |
ISBN | : 9781107366954 |
Tutorial survey papers on important areas of ergodic theory, with related research papers.
Author | : Alexander Gorodnik |
Publisher | : Princeton University Press |
Total Pages | : 136 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 0691141851 |
The results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope. Traditional ergodic theorems focused on amenable groups, and relied on the existence of an asymptotically invariant sequence in the group, the resulting maximal inequalities based on covering arguments, and the transference principle. Here, Alexander Gorodnik and Amos Nevo develop a systematic general approach to the proof of ergodic theorems for a large class of non-amenable locally compact groups and their lattice subgroups. Simple general conditions on the spectral theory of the group and the regularity of the averaging sets are formulated, which suffice to guarantee convergence to the ergodic mean. In particular, this approach gives a complete solution to the problem of establishing mean and pointwise ergodic theorems for the natural averages on semisimple algebraic groups and on their discrete lattice subgroups. Furthermore, an explicit quantitative rate of convergence to the ergodic mean is established in many cases. The topic of this volume lies at the intersection of several mathematical fields of fundamental importance. These include ergodic theory and dynamics of non-amenable groups, harmonic analysis on semisimple algebraic groups and their homogeneous spaces, quantitative non-Euclidean lattice point counting problems and their application to number theory, as well as equidistribution and non-commutative Diophantine approximation. Many examples and applications are provided in the text, demonstrating the usefulness of the results established.
Author | : John J. Benedetto |
Publisher | : CRC Press |
Total Pages | : 668 |
Release | : 2020-03-10 |
Genre | : Mathematics |
ISBN | : 1000674150 |
The Journal of Fourier Analysis and Applications is a journal of the mathematical sciences devoted to Fourier analysis and its applications. The subject of Fourier analysis has had a major impact on the development of mathematics, on the understanding of many engineering and scientific phenomena, and on the solution of some of the most important problems in mathematics and the sciences. At the end of June 1993, a large Conference in Harmonic Analysis was held at the University of Paris-Sud at Orsay to celebrate the prominent role played by Jean-Pierre Kahane and his numerous achievements in this field. The large variety of topics discussed in this meeting, ranging from classical Harmonic Analysis to Probability Theory, reflects the intense mathematical curiosity and the broad mathematical interest of Jean-Pierre Kahane. Indeed, all of them are connected to his work. The mornings were devoted to plenary addresses while up to four parallel sessions took place in the afternoons. Altogether, there were about eighty speakers. This wide range of subjects appears in these proceedings which include thirty six articles.
Author | : Idris Assani |
Publisher | : Walter de Gruyter |
Total Pages | : 288 |
Release | : 2013-12-12 |
Genre | : Mathematics |
ISBN | : 3110298201 |
This is the proceedings of the workshop on recent developments in ergodic theory and dynamical systems on March 2011 and March 2012 at the University of North Carolina at Chapel Hill. The articles in this volume cover several aspects of vibrant research in ergodic theory and dynamical systems. It contains contributions to Teichmuller dynamics, interval exchange transformations, continued fractions, return times averages, Furstenberg Fractals, fractal geometry of non-uniformly hyperbolic horseshoes, convergence along the sequence of squares, adic and horocycle flows, and topological flows. These contributions illustrate the connections between ergodic theory and dynamical systems, number theory, harmonic analysis, probability, and algebra. Two surveys are included which give a nice introduction for interested young or senior researcher to some active research areas. Overall this volume provides a very useful blend of techniques and methods as well as directions of research on general convergence phenomena in ergodic theory and dynamical systems.