Wavelet Analysis

Abstract

Gabor’s method dates from the 1940s. With wavelets we enter a dynamic contemporary research environment; what is now known as the modern theory of wavelets emerged in the 1980s, notably with the article [GM84] by Alex Grossmann and Jean Morlet. We say “modern” wavelet theory because looking back over the mathematical landscape from a late twentieth century perspective we can identify many earlier ideas and techniques that are now logically included in this theory. Work by Haar in 1909; work in the late 1920s by Strömberg; results from the 1930s by Littlewood and Paley, Lusin, and Franklin; and later work in the 1960s, particularly the result of Calderon on operators with singular kernels—all these efforts and others are now interpreted in the language of wavelets.