This text offers an excellent introduction to the mathematical theory of wavelets for senior undergraduate students. Despite the fact that this theory is intrinsically advanced, the author's elementary approach makes it accessible at the undergraduate level. Beginning with thorough accounts of inner product spaces and Hilbert spaces, the book then shifts its focus to wavelets specifically, starting with the Haar wavelet, broadening to wavelets in general, and culminating in the construction of the Daubechies wavelets. All of this is done using only elementary methods, bypassing the use of the Fourier integral transform. Arguments using the Fourier transform are introduced in the final chapter, and this less elementary approach is used to outline a second and quite different construction of the Daubechies wavelets. The main text of the book is supplemented by more than 200 exercises ranging in difficulty and complexity.

'Not only does it bring the subject in a most suitable and systematic way that, I am sure, mathematics students are used to and probably appreciate most. It is also following some good rules of didactics taking the students by the hand and bringing them to a higher level of understanding, ensuring that at least the bulk of the students does not declutch. A lot of effort is put into taking the rungs of the ladder at just the right pace, not boringly slow or not frighteningly fast, and always placing a chapter in the proper context: what has been achieved, and where do we want to go?'

Adhemar Bultheel Source: European Mathematical Society

'What is really nice with this book is its style, which leads the student step by step through different ideas, theorems and proofs. It explains the reason behind new concepts, discusses their shortcomings, and uses these as a motivation to introduce other concepts.'

Salim Salem Source: MAA Reviews