This text, combining analysis and tools from mathematical probability, focuses on a systematic and novel exposition of a recent trend in pure and applied mathematics. The emphasis is on the unity of basis constructions and their expansions (bases which are computationally efficient), and on their use in several areas: from wavelets to fractals. The aim of this book is to show how to use processes from probability, random walks on branches, and their path-space measures in the study of convergence questions from harmonic analysis, with particular emphasis on the infinite products that arise in the analysis of wavelets. The book brings together tools from engineering (especially signal/image processing) and mathematics (harmonic analysis and operator theory).
Key features:
* Interdisciplinary focus addressed to a diverse audience of students and workers in a variety of fields, meeting at the crossroads where they merge
* Hands-on approach with generous motivation
* New pedagogical features to enhance teaching techniques and experience
* Includes more than 34 figures with detailed captions, illustrating the main ideas and visualizing the deeper connections in the subject
* Separate sections explain engineering terms to mathematicians and operator theory to engineers
* Interdisciplinary presentation and approach, combining central ideas from mathematical analysis (with a twist in the direction of operator theory and harmonic analysis), probability, computation, physics, and engineering
The presentation includes numerous exercises that are essential to reinforce fundamental concepts by helping both students and applied users practice sketching functions or iterative schemes, as well as to hone computational skills. Graduate students, researchers, applied mathematicians, engineers and physicists alike will benefit from this unique work in book form that fills a gap in the literature.
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