Abstract
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.
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Strichartz, R. Self-Similarity in Harmonic Analysis. J Fourier Anal Appl 1, 1–37 (1994). https://doi.org/10.1007/s00041-001-4001-z
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DOI: https://doi.org/10.1007/s00041-001-4001-z