Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-22T04:15:48.406Z Has data issue: false hasContentIssue false
  • English
  • Français

U-Sets in Compact, 0-Dimensional, Metric Groups

Published online by Cambridge University Press:  20 November 2018

D. J. Grubb
D. J. Grubb*
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper studies a pointwise definition of sets of uniqueness on compact, 0-dimensional, metric groups. It is shown that this definition is equivalent for closed sets to one based on supports of pseudo functions. An analog of Rajchman's theorem is given leading to examples of sets of uniqueness.

Keywords

43A4642C10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 2 , 01 June 1989 , pp. 149 - 155
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Marke, Bozejko. Sets of uniqueness in noncommutative locally compact groups, Proc. Amer. Math. Soc. 64 (1977), 93-96.Google Scholar
2. Graham, C. C. and McGehee, O. C.. Essays in Commutative Harmonic Analysis, New York, NY: Springer-Verlag New York Inc. 1979.Google Scholar
3. Grubb, D. J.. Summation methods and uniqueness in Vilenkin groups, accepted by Proc. Amer. Math. Soc.Google Scholar
4. Sets of uniqueness in compact, 0-dimensional groups, Trans. Amer. Math. Soc. 301, no. 1 (1987), 239-249.Google Scholar
5. Hewitt, E. and Ross, K. A.. Abstract Harmonic Analysis II, New York, NY: Springer-Verlag New York 1970.Google Scholar
6. Ya Vilenkin, N.. On a class of complete orthonormal systems, Izv. Adak, Nauk SSR, 11 (1947) 363-400, English Translation - Amer. Math. Soc. Translations, Vol. 28, 1–35.Google Scholar
7. Wade, W. R.. Sets of uniqueness for the group of integers of a p-series field, Can. J. Math. Vol. XXXI, No. 4, 1979, pp. 858–866.Google Scholar
8. Yoneda, K.. Summing generalized closed U-Sets for Walsh series, Proc. Amer. Math. Soc. 94 (1985), 110-114.Google Scholar
9. Zygmund, A.. Trigonometric Series, Cambridge, England: Cambridge University Press, 1979.Google Scholar