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Diophantine Approximation and Dirichlet Series. 2nd ed. 2020

種類:
電子ブック
責任表示:
by Hervé Queffélec, Martine Queffélec
出版情報:
Singapore : Springer Nature Singapore : Imprint: Springer, 2020
著者名:
シリーズ名:
Texts and Readings in Mathematics ; 80
ISBN:
9789811593512 [9811593515]  CiNii Books  Calil
注記:
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 ergod
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