03037nam a22003495a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001700168084002200185100002800207245007500235260008200310300003400392336002600426337002600452338003600478347002400514490008300538506006600621520178000687650002402467650004602491650005302537856003202590856006502622105-091109CH-001817-320091109150325.0a fot ||| 0|cr nn mmmmamaa091109e20090829sz fot ||| 0|eng d a978303719546870a10.4171/0462doi ach0018173 7aPBWL2bicssc a37-xxa60-xx2msc1 aWeber, Michel,eauthor.10aDynamical Systems and Processesh[electronic resource] /cMichel Weber3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2009 a1 online resource (773 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aIRMA Lectures in Mathematics and Theoretical Physics (IRMA) ;x2523-5133 ;v141 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThis book presents in a concise and accessible way, as well as in
a common setting, various tools and methods arising from spectral
theory, ergodic theory and stochastic processes theory, which
form the basis of and contribute interactively a great deal to the
current research on almost everywhere convergence problems.
The text is divided into four parts.
Part I is devoted to spectral results such as von Neumann’s theorem, spectral regularizations inequalities and
their link with square functions and entropy numbers of ergodic averages.
The representation of a weakly
stationary process as Fourier transform of some random orthogonal measure,
and a study of Gaposhkin’s
spectral criterion conclude this part.
Classical results such as mixing in dynamical systems,
Birkhoff's pointwise theorem, dominated ergodic theorems,
oscillations functions of ergodic averages, transference
principle, Wiener–Wintner theorem, Banach principle, continuity principle,
Bourgain's entropy criteria, Burton–Denker’s central limit
theorem are covered in part II.
The metric entropy method and the majorizing measure method, including a
succinct study of Gaussian processes, are treated in part III, with
applications to suprema of random polynomials.
Part IV contains a study of Riemann sums and of the convergence
properties of the system {f(nkx), k ≥ 1}, as well as a probabilistic approach concerning divisors with applications.
Researchers working in dynamical systems and at the crossroads of
spectral theory, ergodic theory and stochastic processes will find the
tools, methods and results presented in this book of great interest.
It is written in a style accessible to graduate students throughout.07aStochastics2bicssc07aDynamical systems and ergodic theory2msc07aProbability theory and stochastic processes2msc40uhttps://doi.org/10.4171/046423cover imageuhttps://www.ems-ph.org/img/books/weber_mini.jpg