LEADER 02998oam 2200469 450 001 996418203003316 005 20220401103250.0 010 $a981-15-9351-5 024 7 $a10.1007/978-981-15-9351-2 035 $a(CKB)5590000000433269 035 $a(DE-He213)978-981-15-9351-2 035 $a(MiAaPQ)EBC6465091 035 $a(PPN)253251192 035 $a(EXLCZ)995590000000433269 100 $a20210628d2020 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDiophantine approximation and Dirichlet series /$fHervé Queffelec, Martine Queffelec 205 $aSecond edition. 210 1$aGateway East, Singapore :$cSpringer :$cHindustan Book Agency,$d[2020] 210 4$d©2020 215 $a1 online resource (XIX, 287 p. 12 illus., 3 illus. in color.) 225 1 $aTexts and Readings in Mathematics,$x2366-8717 ;$v80 311 $a981-15-9350-7 327 $a1. A Review of Commutative Harmonic Analysis -- 2. Ergodic Theory and Kronecker?s Theorems -- 3. Diophantine Approximation -- 4. General Properties of Dirichlet Series -- 5. Probabilistic Methods for Dirichlet Series -- 6. Hardy Spaces of Dirichlet Series -- 7. Voronin Type theorems -- 8. Composition Operators on the Space H2 of Dirichlet Series. 330 $aThe second edition of the book includes a new chapter on the study of composition operators on the Hardy space and their complete characterization by Gordon and Hedenmalm. The book is devoted to Diophantine approximation, the analytic theory of Dirichlet series and their composition operators, and connections between these two domains which often occur through the Kronecker approximation theorem and the Bohr lift. The book initially discusses Harmonic analysis, including a sharp form of the uncertainty principle, Ergodic theory and Diophantine approximation, basics on continued fractions expansions, and the mixing property of the Gauss map and goes on to present the general theory of Dirichlet series with classes of examples connected to continued fractions, Bohr lift, sharp forms of the Bohnenblust?Hille theorem, Hardy?Dirichlet spaces, composition operators of the Hardy?Dirichlet space, and much more. Proofs throughout the book mix Hilbertian geometry, complex and harmonic analysis, number theory, and ergodic theory, featuring the richness of analytic theory of Dirichlet series. This self-contained book benefits beginners as well as researchers. . 410 0$aTexts and Readings in Mathematics,$x2366-8717 ;$v80 606 $aDiophantine approximation 615 0$aDiophantine approximation. 676 $a512.73 700 $aQuefflec$b Herv$0731205 702 $aQuefflec$b Martine 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bUtOrBLW 906 $aBOOK 912 $a996418203003316 996 $aDiophantine Approximation and Dirichlet Series$92513565 997 $aUNISA