Fundamental Papers in Wavelet Theory

This is a lovely collection of papers coming out of the last two or three decades of mathematical trends connected in one way or the other to wavelets. A current 2006 google search on "wavelet" yields 6,470,000 hits; many of them dealing with applications, for example signal and image processing. The volume brings to light even more interdisciplinary trends. I expect the book will be a valued source for students in math, in applications, and in engineering. The book is divided into seven parts, and each part is given an attractive and well written introduction, written by an expert in the field. Several of the selected papers have served as precursors for major advances in one or the other of the central areas of the subject. The Foreword is written especially for students and it is by Ingrid Daubechies. The individual authors who wrote the seven current and separate introductions to the seven parts of the book are Jelena Kovacevic (signal processing), Jean-Pierre Antoine (physics, coherent states), Hans Feichtinger (precursors of wavelet bases), Yves Meyer (harmonic analysis and atomic decompositions), Guido Weiss (multiresolutions, multivariable theory), and Mladen V. Wickerhauser (applications, computations, image coding and more.) And there is a charming introduction to the entire collection written by John Benedetto. It is delightful and full of insight. The historical comments are fascination too. The editor Chris Heil did a wonderful job: The present selection of original papers in the area is meant to offer motivation, and history; and more importantly it serves as a guide to students trying to learn some of this. The chosen papers are on target, and each section is nicely introduced so that it will help students getting into anyone of the many aspects of wavelet mathematics. Some of the original and older papers (Haar, Meyer, ...) were in French or German, and they have now been translated. Excellent translations! The total number of pages is a little less than 900, but even so, there is a lot more to say, for example about connections to computer graphics. Review by Palle Jorgensen, October 2006.

This is a lovely collection of papers coming out of the last two or three decades of mathematical trends connected in one way or the other to wavelets. A current 2006 google search on "wavelet" yields 6,470,000 hits; many of them dealing with applications, for example signal and image processing. The volume brings to light even more interdisciplinary trends. I expect the book will be a valued source for students in math, in applications, and in engineering. The book is divided into seven parts, and each part is given an attractive and well written introduction, written by an expert in the field. Several of the selected papers have served as precursors for major advances in one or the other of the central areas of the subject. The Foreword is written especially for students and it is by Ingrid Daubechies. The individual authors who wrote the seven current and separate introductions to the seven parts of the book are Jelena Kovacevic (signal processing), Jean-Pierre Antoine (physics, coherent states), Hans Feichtinger (precursors of wavelet bases), Yves Meyer (harmonic analysis and atomic decompositions), Guido Weiss (multiresolutions, multivariable theory), and Mladen V. Wickerhauser (applications, computations, image coding and more.) And there is a charming introduction to the entire collection written by John Benedetto. It is delightful and full of insight. The historical comments are fascination too. The editor Chris Heil did a wonderful job: The present selection of original papers in the area is meant to offer motivation, and history; and more importantly it serves as a guide to students trying to learn some of this. The chosen papers are on target, and each section is nicely introduced so that it will help students getting into anyone of the many aspects of wavelet mathematics. Some of the original and older papers (Haar, Meyer, ...) were in French or German, and they have now been translated. Excellent translations! The total number of pages is a little less than 900, but even so, there is a lot more to say, for example about connections to computer graphics. Review by Palle Jorgensen, October 2006.