This textbook covers four research directions in harmonic analysis and presents some of its latest applications. It is the first work that combines spline theory, wavelets, frames, and time-frequency methods up to construction on manifolds other than Rn.

This state-of-the-art textbook covers four research directions in harmonic analysis and presents some of its latest applications. It is the first work that combines spline theory, wavelets, frames, and time-frequency methods up to construction on manifolds other then Rn.

Written by internationally renowned mathematicians, the work's main emphasis is on the interdependence of the four modern research directions. Each chapter ends with exercises that allow for a more in-depth understanding of the material and are intended to stimulate the reader toward further research.

Four Short Courses in Harmonic Analysis is intended as a graduate-level textbook for a course in harmonic analysis. It is also an excellent reference guide for researchers and practitioners with diverse mathematical backgrounds, including theoretical and applied mathematics, image and signal processing engineering, and communication theory.

The first work to combine spline theory, wavelets, frames, and time-frequency methods up to construction on manifolds other then Rn Written by world-renowned experts in harmonic analysis Main emphasis is on interdependence of the four modern research directions in harmonic analysis covered in the book Exercises at the end of each chapter Intended as a graduate-level textbook for a courses on harmonic analysis and related areas Includes supplementary material: sn.pub/extras

Inhalt
Introduction: Mathematical Aspects of Time-Frequency Analysis.- B-Spline Generated Frames.- Continuous and Discrete Reproducing Systems That Arise from Translations. Theory and Applications of Composite Wavelets.- Wavelets on the Sphere.- Wiener's Lemma: Theme and Variations. An Introduction to Spectral Invariance and Its Applications.