000			01949 a2200277 4500
999			_c55429 _d55429
008			210911b ||||| |||| 00| 0 eng d
020			_a9789386279828
082			_a512.73 _bQUE
100			_aQueffélec, Hervé
245			_aDiophantine approximation and dirichlet series
250			_a2nd ed.
260			_bHindustan Book Agency, _c2021 _aNew Delhi:
300			_aix, 287p ; _bpb. ; _c24cm.
365			_aINR _b670.00
440			_aText and Readings in Mathematics
504			_aIncludes bibliography and index
520			_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
650			_aDiophantine approximation
650			_aDirichlet series
650			_aMathematics
650			_aVibration
650			_aDynamics
650			_aErgodic theory
700			_aQueffélec, Martine _eCo-author
942			_2ddc _cTD