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Diophantine Approximation and Dirich...

Queffelec, Herve.

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Diophantine Approximation and Dirichlet Series

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Diophantine Approximation and Dirichlet Series/ by Herve Queffelec, Martine Queffelec.
作者:	Queffelec, Herve.
其他作者:	Queffelec, Martine.
出版者:	Singapore :Springer Singapore : : 2020.,
面頁冊數:	xix, 287 p. :ill. (some col.), digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Diophantine approximation. -
電子資源:	https://doi.org/10.1007/978-981-15-9351-2
ISBN:	9789811593512

Diophantine Approximation and Dirichlet Series
Queffelec, Herve.

Diophantine Approximation and Dirichlet Series[electronic resource] /by Herve Queffelec, Martine Queffelec. - Second edition. - Singapore :Springer Singapore :2020. - xix, 287 p. :ill. (some col.), digital ;24 cm. - Texts and readings in mathematics,v.802366-8717 ;. - Texts and readings in mathematics ;v.80..

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.

ISBN: 9789811593512

Standard No.: 10.1007/978-981-15-9351-2doiSubjects--Topical Terms:

705002
Diophantine approximation.

LC Class. No.: QA242 / .Q84 2020

Dewey Class. No.: 512.73

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505 0 $a 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.
520 $a 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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