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The classical subject of bases in Banach spaces has taken on a new life in the modern development of applied harmonic analysis. This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and its use in both applied and classical harmonic analysis.

The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory.

* Part I develops the functional analysis that underlies most of the concepts presented in the later parts of the text.

* Part II presents...

This text is a self-contained introduction to the three main families that we encounter in analysis - metric spaces, normed spaces, and inner product spaces - and to the operators that transform objects in one into objects in another. With an emphasis on the fundamental properties defining the spaces, this book guides readers to a deeper understanding of analysis and an appreciation of the field as the "science of functions."

Many important topics that are rarely presented in an accessible way to undergraduate students are included, such as unconditional convergence...

This book traces the prehistory and initial development of wavelet theory, a discipline that has had a profound impact on mathematics, physics, and engineering. Interchanges between these fields during the last fifteen years have led to a number of advances in applications such as image compression, turbulence, machine vision, radar, and earthquake prediction.

This book contains the seminal papers that presented the ideas from which wavelet theory evolved, as well as those major papers that developed the theory into its current form. These papers originated in a variety of...