| Titre : |
Hilbert transforms. Volume 1 |
| Type de document : |
texte imprimé |
| Auteurs : |
Frederick W. (1947-....) King, Auteur |
| Editeur : |
Cambridge : Cambridge University Press |
| Année de publication : |
2009 |
| Collection : |
Encyclopedia of mathematics and its applications, ISSN 0953-4806 |
| Importance : |
XXXVIII-858, XXXVIII-660 p. |
| Présentation : |
ill. |
| Format : |
24 cm. |
| ISBN/ISSN/EAN : |
978-0-521-88762-5 |
| Note générale : |
Bibliogr. p. 745-823. - Index |
| Langues : |
Anglais (eng) |
| Mots-clés : |
Hilbert transform
Hilbert, Transformation de |
| Index. décimale : |
517.3 Calcul intégral. Intégration |
| Résumé : |
The Hilbert transform has many uses, including solving problems in aerodynamics, condensed matter physics, optics, fluids, and engineering. Written in a style that will suit a wide audience (including the physical sciences), this book will become the reference of choice on the topic, whatever the subject background of the reader. It explains all the common Hilbert transforms, mathematical techniques for evaluating them, and has detailed discussions of their application. Especially useful for researchers are the tabulation of analytically evaluated Hilbert transforms, and an atlas that immediately illustrates how the Hilbert transform alters a function. A collection of exercises helps the reader to test their understanding of the material in each chapter. The bibliography is a wide-ranging collection of references both to the classical mathematical papers, and to a diverse array of applications. |
| Note de contenu : |
Summary :
Volume I: 1. Introduction
2. Review of some background mathematics
3. Derivation of the Hilbert transform relations.
4. Some basic properties of the Hilbert transform
5. Relationship between the Hilbert transform and some common transforms
6. The Hilbert transform of periodic functions
7. Inequalities for the Hilbert transform
8. Asymptotic behavior of the Hilbert transform
9. Hilbert transforms of some special functions
10. Hilbert transforms involving distributions
11. The finite Hilbert transform
12. Some singular integral equations
13. Discrete Hilbert transforms
14. Numerical evaluation of Hilbert transforms |
Hilbert transforms. Volume 1 [texte imprimé] / Frederick W. (1947-....) King, Auteur . - Cambridge : Cambridge University Press, 2009 . - XXXVIII-858, XXXVIII-660 p. : ill. ; 24 cm.. - ( Encyclopedia of mathematics and its applications, ISSN 0953-4806) . ISBN : 978-0-521-88762-5 Bibliogr. p. 745-823. - Index Langues : Anglais ( eng)
| Mots-clés : |
Hilbert transform
Hilbert, Transformation de |
| Index. décimale : |
517.3 Calcul intégral. Intégration |
| Résumé : |
The Hilbert transform has many uses, including solving problems in aerodynamics, condensed matter physics, optics, fluids, and engineering. Written in a style that will suit a wide audience (including the physical sciences), this book will become the reference of choice on the topic, whatever the subject background of the reader. It explains all the common Hilbert transforms, mathematical techniques for evaluating them, and has detailed discussions of their application. Especially useful for researchers are the tabulation of analytically evaluated Hilbert transforms, and an atlas that immediately illustrates how the Hilbert transform alters a function. A collection of exercises helps the reader to test their understanding of the material in each chapter. The bibliography is a wide-ranging collection of references both to the classical mathematical papers, and to a diverse array of applications. |
| Note de contenu : |
Summary :
Volume I: 1. Introduction
2. Review of some background mathematics
3. Derivation of the Hilbert transform relations.
4. Some basic properties of the Hilbert transform
5. Relationship between the Hilbert transform and some common transforms
6. The Hilbert transform of periodic functions
7. Inequalities for the Hilbert transform
8. Asymptotic behavior of the Hilbert transform
9. Hilbert transforms of some special functions
10. Hilbert transforms involving distributions
11. The finite Hilbert transform
12. Some singular integral equations
13. Discrete Hilbert transforms
14. Numerical evaluation of Hilbert transforms |
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