Self-Similarity in Harmonic Analysis
- Cite this article as:
- Strichartz, R. J Fourier Anal Appl (1994) 1: 1. doi:10.1007/s00041-001-4001-z
This is a survey of recent work involving concepts of self-similarity that relate to harmonic analysis. Perhaps the main theme is the question: how does the fractal or self-similar nature of an object express itself on the Fourier transform side? A wide range of related topics are discussed, including self-similar measures and distributions, fractal Plancherel theorems, Lp dimensions and densities of measures, multiperiodic functions and their asymptotic behavior, convolution equations with self-similar measures, self-similar tilings, and the development of self-similar analysis on stratified nilpotent Lie groups.