By Christopher Heil

The classical topic of bases in Banach areas has taken on a brand new existence within the sleek improvement of utilized harmonic research. This textbook is a self-contained creation to the summary idea of bases and redundant body expansions and its use in either utilized and classical harmonic analysis.

The 4 components of the textual content take the reader from classical sensible research and foundation thought to fashionable time-frequency and wavelet theory.

* half I develops the useful research that underlies lots of the techniques offered within the later elements of the text.

* half II offers the summary idea of bases and frames in Banach and Hilbert areas, together with the classical issues of convergence, Schauder bases, biorthogonal platforms, and unconditional bases, by means of the more moderen issues of Riesz bases and frames in Hilbert spaces.

* half III relates bases and frames to utilized harmonic research, together with sampling thought, Gabor research, and wavelet theory.

* half IV offers with classical harmonic research and Fourier sequence, emphasizing the function performed by means of bases, that is a unique perspective from that taken in such a lot discussions of Fourier series.

Key features:

* Self-contained presentation with transparent proofs obtainable to graduate scholars, natural and utilized mathematicians, and engineers attracted to the mathematical underpinnings of applications.

* huge routines supplement the textual content and supply possibilities for learning-by-doing, making the textual content appropriate for graduate-level classes; tricks for chosen routines are incorporated on the finish of the book.

* A separate options guide is offered for teachers upon request at: www.birkhauser-science.com/978-0-8176-4686-8/.

* No different textual content develops the binds among classical foundation thought and its sleek makes use of in utilized harmonic analysis.

*A foundation conception Primer* is acceptable for self sufficient research or because the foundation for a graduate-level path. teachers have numerous suggestions for construction a path round the textual content looking on the extent and heritage in their students.