LEADER 04405nam 2200781Ia 450 001 9910456597903321 005 20200520144314.0 010 $a1-282-30380-5 010 $a9786612303807 010 $a1-4008-3106-7 024 7 $a10.1515/9781400831067 035 $a(CKB)2550000000002880 035 $a(EBL)475845 035 $a(OCoLC)507428541 035 $a(SSID)ssj0000337335 035 $a(PQKBManifestationID)11297311 035 $a(PQKBTitleCode)TC0000337335 035 $a(PQKBWorkID)10287892 035 $a(PQKB)10258020 035 $a(MiAaPQ)EBC475845 035 $a(DE-B1597)446614 035 $a(OCoLC)979685624 035 $a(DE-B1597)9781400831067 035 $a(PPN)15099625X 035 $a(Au-PeEL)EBL475845 035 $a(CaPaEBR)ebr10333494 035 $a(CaONFJC)MIL230380 035 $a(EXLCZ)992550000000002880 100 $a20090202d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe ergodic theory of lattice subgroups$b[electronic resource] /$fAlexander Gorodnik and Amos Nevo 205 $aCourse Book 210 $aPrinceton, N.J. $cPrinceton University Press$d2009 215 $a1 online resource (136 p.) 225 1 $aAnnals of mathematics studies ;$vno. 172 300 $aDescription based upon print version of record. 311 $a0-691-14184-3 311 $a0-691-14185-1 320 $aIncludes bibliographical references and index. 327 $t Frontmatter -- $tContents -- $tPreface -- $tChapter One. Main results: Semisimple Lie groups case -- $tChapter Two. Examples and applications -- $tChapter Three. Definitions, preliminaries, and basic tools -- $tChapter Four. Main results and an overview of the proofs -- $tChapter Five. Proof of ergodic theorems for S-algebraic groups -- $tChapter Six. Proof of ergodic theorems for lattice subgroups -- $tChapter Seven. Volume estimates and volume regularity -- $tChapter Eight. Comments and complements -- $tBibliography -- $tIndex 330 $aThe results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope. Traditional ergodic theorems focused on amenable groups, and relied on the existence of an asymptotically invariant sequence in the group, the resulting maximal inequalities based on covering arguments, and the transference principle. Here, Alexander Gorodnik and Amos Nevo develop a systematic general approach to the proof of ergodic theorems for a large class of non-amenable locally compact groups and their lattice subgroups. Simple general conditions on the spectral theory of the group and the regularity of the averaging sets are formulated, which suffice to guarantee convergence to the ergodic mean. In particular, this approach gives a complete solution to the problem of establishing mean and pointwise ergodic theorems for the natural averages on semisimple algebraic groups and on their discrete lattice subgroups. Furthermore, an explicit quantitative rate of convergence to the ergodic mean is established in many cases. The topic of this volume lies at the intersection of several mathematical fields of fundamental importance. These include ergodic theory and dynamics of non-amenable groups, harmonic analysis on semisimple algebraic groups and their homogeneous spaces, quantitative non-Euclidean lattice point counting problems and their application to number theory, as well as equidistribution and non-commutative Diophantine approximation. Many examples and applications are provided in the text, demonstrating the usefulness of the results established. 410 0$aAnnals of mathematics studies ;$vno. 172. 606 $aErgodic theory 606 $aLie groups 606 $aLattice theory 606 $aHarmonic analysis 606 $aDynamics 608 $aElectronic books. 615 0$aErgodic theory. 615 0$aLie groups. 615 0$aLattice theory. 615 0$aHarmonic analysis. 615 0$aDynamics. 676 $a515/.48 686 $aSI 830$2rvk 700 $aGorodnik$b Alexander$f1975-$01057408 701 $aNevo$b Amos$f1966-$01057409 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910456597903321 996 $aThe ergodic theory of lattice subgroups$92492664 997 $aUNINA