Journal of Fourier Analysis and Applications

, Volume 1, Issue 1, pp 1–37

Self-Similarity in Harmonic Analysis

  • Robert S. Strichartz
Survey Article

DOI: 10.1007/s00041-001-4001-z

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.

Copyright information

© Birkhäuser Boston 1994

Authors and Affiliations

  • Robert S. Strichartz
    • 1
  1. 1.Mathematics Department, White Hall, Cornell University, Ithaca, New York 14853USA