U-Sets in Compact, 0-Dimensional, Metric Groups
Canadian mathematical bulletin, Tome 32 (1989) no. 2, pp. 149-155

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1989-022-2
Mots-clés : 43A46, 42C10
Grubb, D. J. U-Sets in Compact, 0-Dimensional, Metric Groups. Canadian mathematical bulletin, Tome 32 (1989) no. 2, pp. 149-155. doi: 10.4153/CMB-1989-022-2
@article{10_4153_CMB_1989_022_2,
     author = {Grubb, D. J.},
     title = {U-Sets in {Compact,} {0-Dimensional,} {Metric} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {149--155},
     year = {1989},
     volume = {32},
     number = {2},
     doi = {10.4153/CMB-1989-022-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1989-022-2/}
}
TY  - JOUR
AU  - Grubb, D. J.
TI  - U-Sets in Compact, 0-Dimensional, Metric Groups
JO  - Canadian mathematical bulletin
PY  - 1989
SP  - 149
EP  - 155
VL  - 32
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1989-022-2/
DO  - 10.4153/CMB-1989-022-2
ID  - 10_4153_CMB_1989_022_2
ER  - 
%0 Journal Article
%A Grubb, D. J.
%T U-Sets in Compact, 0-Dimensional, Metric Groups
%J Canadian mathematical bulletin
%D 1989
%P 149-155
%V 32
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1989-022-2/
%R 10.4153/CMB-1989-022-2
%F 10_4153_CMB_1989_022_2

[1] 1. Marke, Bozejko. Sets of uniqueness in noncommutative locally compact groups, Proc. Amer. Math. Soc. 64 (1977), 93-96. Google Scholar

[2] 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] 3. Grubb, D. J.. Summation methods and uniqueness in Vilenkin groups, accepted by Proc. Amer. Math. Soc. Google Scholar

[4] 4. Sets of uniqueness in compact, 0-dimensional groups, Trans. Amer. Math. Soc. 301, no. 1 (1987), 239-249. Google Scholar

[5] 5. Hewitt, E. and Ross, K. A.. Abstract Harmonic Analysis II, New York, NY: Springer-Verlag New York 1970. Google Scholar

[6] 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] 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] 8. Yoneda, K.. Summing generalized closed U-Sets for Walsh series, Proc. Amer. Math. Soc. 94 (1985), 110-114. Google Scholar

[9] 9. Zygmund, A.. Trigonometric Series, Cambridge, England: Cambridge University Press, 1979. Google Scholar

Cité par Sources :