The tools that we need to develop the abstract theory of bases and frames are largely drawn from the field of functional analysis. Therefore, the first two chapters of this volume survey the basic definitions and theorems fromfunctional analysis that will be used throughout this volume. This chapter reviews foundational material that is likely to be at least partially familiar to most readers, while Chapter 2 delves into more advanced topics in functional analysis.

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Authors and Affiliations

1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA

   Christopher Heil

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Correspondence toChristopher Heil.

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