Hilbert Transforms: Volume 2: 125 (Encyclopedia of Mathematics and its Applications, Series Number 125)
Cambridge University Press, 4/27/2009
EAN 9780521517201, ISBN10: 0521517206
Hardcover, 698 pages, 23.4 x 15.6 x 3.8 cm
Language: English
Originally published in English
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.
Preface
List of symbols
List of abbreviations
Volume II
15. Hilbert transforms in En
16. Some further extensions of the classical Hilbert transform
17. Linear systems and causality
18. The Hilbert transform of waveforms and signal processing
19. Kramers–Kronig relations
20. Dispersion relations for some linear optical properties
21. Dispersion relations for magneto-optical and natural optical activity
22. Dispersion relations for nonlinear optical properties
23. Some further applications of Hilbert transforms
Appendix 1. Table of selected Hilbert transforms
Appendix 2. Atlas of selected Hilbert transform pairs
References
Subject index
Author index.
'... every scientist dealing with the Hilbert transform in his or her research will find valuable material in this work.' Lasha Ephremidze, Mathematical Reviews