Document Detail

Lacunarity for compact groups.
MedLine Citation:
PMID:  16591896     Owner:  NLM     Status:  PubMed-not-MEDLINE    
Let G be a compact Abelian group with character group X. A subset Delta of X is called a [unk](q) set (1 < q < infinity) if for all trigonometric polynomials f = [unk](k=1) (n) alpha(k)chi(k) (chi(1),...,chi(n) [unk] Delta) an inequality parallelf parallel(q) [unk] [unk] parallelf parallel(1) obtains, where [unk] is a positive constant depending only on Delta. The subset Delta is called a Sidon set if every bounded function on Delta can be matched by a Fourier-Stieltjes transform. It is known that every Sidon set is a [unk](q) set for all q. For G = T, X = Z, Rudin (J. Math. Mech., 9, 203 (1960)) has found a set that is [unk](q) for all q but not Sidon. We extend this result to all infinite compact Abelian groups G: the character group X contains a subset Delta that is [unk](q) for all q, 1 < q < infinity, but Delta is not a Sidon set.
R E Edwards; E Hewitt; K A Ross
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Publication Detail:
Type:  Journal Article    
Journal Detail:
Title:  Proceedings of the National Academy of Sciences of the United States of America     Volume:  68     ISSN:  0027-8424     ISO Abbreviation:  Proc. Natl. Acad. Sci. U.S.A.     Publication Date:  1971 Jan 
Date Detail:
Created Date:  2010-06-29     Completed Date:  2010-06-29     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  7505876     Medline TA:  Proc Natl Acad Sci U S A     Country:  United States    
Other Details:
Languages:  eng     Pagination:  25     Citation Subset:  -    
Australian National University, Canberra.
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