Author: Joseph Rosenblatt
Publisher: American Mathematical Soc.
ISBN: 0821842358
Category : Mathematics
Languages : en
Pages : 242
Book Description
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.
Topics in Harmonic Analysis and Ergodic Theory
Author: Joseph Rosenblatt
Publisher: American Mathematical Soc.
ISBN: 0821842358
Category : Mathematics
Languages : en
Pages : 242
Book Description
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.
Publisher: American Mathematical Soc.
ISBN: 0821842358
Category : Mathematics
Languages : en
Pages : 242
Book Description
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.
Ergodic Theory and Its Connection with Harmonic Analysis
Author: Karl Endel Petersen
Publisher: Cambridge University Press
ISBN: 0521459990
Category : Ergodic theory
Languages : en
Pages : 452
Book Description
Tutorial survey papers on important areas of ergodic theory, with related research papers.
Publisher: Cambridge University Press
ISBN: 0521459990
Category : Ergodic theory
Languages : en
Pages : 452
Book Description
Tutorial survey papers on important areas of ergodic theory, with related research papers.
Ergodic Theory and Harmonic Analysis
Author: Karl Endel Petersen
Publisher:
ISBN: 9781107362048
Category : MATHEMATICS
Languages : en
Pages : 450
Book Description
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.
Publisher:
ISBN: 9781107362048
Category : MATHEMATICS
Languages : en
Pages : 450
Book Description
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.
Investigations in Harmonic Analysis, Ergodic Theory, and Related Topics in Analysis
Author: H. Furstenberg
Publisher:
ISBN:
Category :
Languages : en
Pages : 15
Book Description
A number of problems in harmonic analysis as well as in some related domains of analysis are considered. These include problems arising in trying to extend classical harmonic analysis to non-commutative groups, as well as problems arising within the classical framework. (Author).
Publisher:
ISBN:
Category :
Languages : en
Pages : 15
Book Description
A number of problems in harmonic analysis as well as in some related domains of analysis are considered. These include problems arising in trying to extend classical harmonic analysis to non-commutative groups, as well as problems arising within the classical framework. (Author).
The Ergodic Theory of Lattice Subgroups (AM-172)
Author: Alexander Gorodnik
Publisher: Princeton University Press
ISBN: 0691141851
Category : Mathematics
Languages : en
Pages : 136
Book Description
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.
Publisher: Princeton University Press
ISBN: 0691141851
Category : Mathematics
Languages : en
Pages : 136
Book Description
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.
Ergodic Theory and Harmonic Analysis
Author: Karl E. Petersen
Publisher:
ISBN: 9781107366954
Category : Electronic books
Languages : en
Pages : 448
Book Description
Tutorial survey papers on important areas of ergodic theory, with related research papers.
Publisher:
ISBN: 9781107366954
Category : Electronic books
Languages : en
Pages : 448
Book Description
Tutorial survey papers on important areas of ergodic theory, with related research papers.
Topics in Ergodic Theory
Author: William Parry
Publisher: Cambridge University Press
ISBN: 9780521604901
Category : Mathematics
Languages : en
Pages : 128
Book Description
An introduction to topics and examples of ergodic theory, a central area of pure mathematics.
Publisher: Cambridge University Press
ISBN: 9780521604901
Category : Mathematics
Languages : en
Pages : 128
Book Description
An introduction to topics and examples of ergodic theory, a central area of pure mathematics.
Ergodic Theory and Dynamical Systems
Author: Idris Assani
Publisher: Walter de Gruyter
ISBN: 3110298201
Category : Mathematics
Languages : en
Pages : 288
Book Description
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.
Publisher: Walter de Gruyter
ISBN: 3110298201
Category : Mathematics
Languages : en
Pages : 288
Book Description
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.
An Introduction to Harmonic Analysis
Author: Yitzhak Katznelson
Publisher: Cambridge University Press
ISBN: 9780521543590
Category : Mathematics
Languages : en
Pages : 342
Book Description
Publisher description
Publisher: Cambridge University Press
ISBN: 9780521543590
Category : Mathematics
Languages : en
Pages : 342
Book Description
Publisher description
Special Issue on Ergodic Theory and Harmonic Analysis
Author: S. C. Bagchi
Publisher:
ISBN:
Category : Ergodic theory
Languages : en
Pages : 440
Book Description
Publisher:
ISBN:
Category : Ergodic theory
Languages : en
Pages : 440
Book Description