Diophantine Approximation and Dirichlet Series
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Beschreibung
The 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.
The 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.
Includes a new chapter on the study of composition operators on the Hardy spaces Combines different aspects of Dirichlet series in a way not presented before in other publications Constructs rigorous mathematical approach towards Diophantine approximation and Dirichlet series
Autor*in
Hervé Queffélec
Themen in »Diophantine Approximation and Dirichlet Series«
Diophantine approximation Gauss Dirichlet series Bohr point Hardy-Dirichlet spaces Bagchi-Voronin theorems r-tuples ergodic theory Rudin-Shapiro Thue-Morse compact operator
Stimmen zu »Diophantine Approximation and Dirichlet Series«
“This high quality textbook and research-level monograph is a reissue of the authors’ book of the same title. … the authors of this book present deeper theorems in Dirichlet series and their Hardy spaces, for which the proofs and references are given. … The bibliography of the 2nd extended edition has 202 records. The book closes with a subject index.” (Nikolaj M. Glazunov, zbMATH 1478.11002, 2022)
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