Diophantine approximation and Dirichlet series
1. 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. Compositio...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Singapore
Springer
2020
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| Ausgabe: | Second edition |
| Schriftenreihe: | Texts and readings in mathematics
volume 80 |
| Schlagworte: | |
| Online Zugang: | zbMATH |
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Tag hinzufügen | Zusammenfassung: | 1. 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. 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. . |
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| Beschreibung: | xix, 287 Seiten Illustrationen |
| ISBN: | 9789811593505 978-981-15-9350-5 |