A Basis Theory Primer: Expanded Edition
This textbook is a mathematical introduction to the theory of bases in Banach spaces, also weaving in the theory of bases in Hilbert spaces and generalizations of bases such as frames. A new impetus for the study of bases in Banach spaces has come from the rise of wavelet theory, and especially the theory of frames, which allow basis-like but possibly redundant expansions.
This is a text to learn from, with detailed explanations of abstract material that are usually explained with the remark "clearly ..." Covering abstract material with a high degree of relevance to a wide variety of modern topics, the book is primarily aimed at mathematicians, but will also encourage engineers to venture into new directions. Exercises at the end of each chapter make the work suitable as a textbook for a variety of graduate-level courses on bases and frames.
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