A Basis Theory Primer: Expanded Edition

ANHA Series Preface.- Preface.- General Notation.- Part I. A Primer on Functional Analysis .- Banach Spaces and Operator Theory.- Functional Analysis.- Part II. Bases and Frames .- Unconditional Convergence of Series in Banach and Hilbert Spaces.- Bases in Banach Spaces.- Biorthogonality, Minimality, and More About Bases.- Unconditional Bases in Banach Spaces.- Bessel Sequences and Bases in Hilbert Spaces.- Frames in Hilbert Spaces.- Part III. Bases and Frames in Applied Harmonic Analysis .- The Fourier Transform on the Real Line.- Sampling, Weighted Exponentials, and Translations.- Gabor Bases and Frames.- Wavelet Bases and Frames.- Part IV. Fourier Series .- Fourier Series.- Basic Properties of Fourier Series.- Part V. Appendices .- Lebesgue Measure and Integration.- Compact and Hilbert-Schmidt Operators.- Hints for Exercises.- Index of Symbols.- References.- Index.