By Bjorn Jawerth, and Guido Weiss Michael Frazier
Littlewood-Paley concept was once built to review functionality areas in harmonic research and partial differential equations. lately, it has contributed to the improvement of the $\varphi$-transform and wavelet decompositions. in accordance with lectures awarded on the NSF-CBMS neighborhood examine convention on Harmonic research and serve as areas, held at Auburn college in July 1989, this booklet is geared toward mathematicians, in addition to mathematically literate scientists and engineers drawn to harmonic research or wavelets. The authors supply not just a common realizing of the world of harmonic research on the subject of Littlewood-Paley conception and atomic and wavelet decompositions, but additionally a few motivation and heritage worthwhile in realizing the new thought of wavelets. The e-book starts with a few basic examples which offer an summary of the classical Littlewood-Paley idea. The $\varphi$-transform, wavelet, and gentle atomic expansions are provided as typical extensions of the classical thought. ultimately, functions to harmonic research (Calderon-Zygmund operators), sign processing (compression), and mathematical physics (potential idea) are mentioned.