LEADER 03688nam 22006615 450 001 9911035054403321 005 20251030120421.0 010 $a3-032-03899-5 024 7 $a10.1007/978-3-032-03899-9 035 $a(CKB)41986926800041 035 $a(MiAaPQ)EBC32384259 035 $a(Au-PeEL)EBL32384259 035 $a(DE-He213)978-3-032-03899-9 035 $a(EXLCZ)9941986926800041 100 $a20251030d2025 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aUnitary Representations and Unitary Duals /$fby Manfred Einsiedler, Thomas Ward 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (578 pages) 225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v308 311 08$a3-032-03898-7 327 $a1 Unitary Representations -- 2 Abelian Groups -- 3 Compact Groups -- 4 Lie Algebras and Unitary Representations of SU2(R) -- 5 Normal Abelian Subgroups and Unitary Duals -- 6 Weak Containment and the Fell Topology -- 7 Smooth Vectors and Decay for SL3(R) -- 8 Discrete Series Representations and Temperedness -- 9 Unitary Representations of SL2(R) -- Appendix A: Linear Algebra -- Appendix B: Analysis -- Appendix C: Topological Groups. 330 $aThis graduate textbook introduces the unitary representation theory of groups, emphasizing applications in fields like dynamical systems. It begins with the general theory and motivation, then explores key classes of groups. Abelian and compact groups are treated through Pontryagin duality and the Peter?Weyl theorem. Metabelian groups illustrate links to ergodic theory and lead to the Mackey machine. Weak containment and the Fell topology are introduced through examples. The final chapters apply the theory to special linear groups in dimensions two and three, covering smooth vectors, spectral gaps, and decay of matrix coefficients. The two-dimensional case is examined in depth, including the Kunze?Stein phenomenon, spectral decomposition on the hyperbolic plane, and the Weil representation. The book concludes with a full description of the unitary dual of SL(2,R) and its Fell topology, applying the theory to prove effective equidistribution of horocycle orbits. With its focus on key examples and concrete explanations, this textbook is aimed at graduate students taking first steps in unitary representation theory. It builds the theory from the ground up, requiring only some familiarity with functional analysis beyond standard undergraduate mathematics. 410 0$aGraduate Texts in Mathematics,$x2197-5612 ;$v308 606 $aTopological groups 606 $aLie groups 606 $aHarmonic analysis 606 $aDynamics 606 $aFunctional analysis 606 $aTopological Groups and Lie Groups 606 $aAbstract Harmonic Analysis 606 $aDynamical Systems 606 $aFunctional Analysis 615 0$aTopological groups. 615 0$aLie groups. 615 0$aHarmonic analysis. 615 0$aDynamics. 615 0$aFunctional analysis. 615 14$aTopological Groups and Lie Groups. 615 24$aAbstract Harmonic Analysis. 615 24$aDynamical Systems. 615 24$aFunctional Analysis. 676 $a512.55 676 $a512.482 700 $aEinsiedler$b Manfred$0477516 701 $aWard$b Thomas$0329535 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911035054403321 996 $aUnitary Representations and Unitary Duals$94451928 997 $aUNINA