Thin sets of harmonic analysis and infinite combinatorics. (English) Zbl 0835.42001
This very scholarly article surveys the appearance of thin sets in research on trigonometric, Rademacher, and Walsh series. It contains new results, new interpretations of old results, and a chart which gives complete answers to ten basic questions about thin sets. It also ends with several open problems and unanswered questions. One small drawback. Although the authors and journals in the six page bibliography have been translated into English, the titles of most of the Russian papers have not.
Reviewer: W.R.Wade (Knoxville)
MSC:
42-02 | Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces |
43A46 | Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) |
42A20 | Convergence and absolute convergence of Fourier and trigonometric series |
42A63 | Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization |
42C15 | General harmonic expansions, frames |