A Note on Sidon Sets in Bounded Orthonormal Systems
نویسندگان
چکیده
منابع مشابه
On Multiplicative Sidon Sets
Fix integers b > a ≥ 1 with g := gcd(a, b). A set S ⊆ N is {a, b}-multiplicative if ax 6= by for all x, y ∈ S. For all n, we determine an {a, b}-multiplicative set with maximum cardinality in [n], and conclude that the maximum density of an {a, b}-multiplicative set is b b+g . Erdős [2, 3, 4] defined a set S ⊆ N to be multiplicative Sidon1 if ab = cd implies {a, b} = {c, d} for all a, b, c, d ∈...
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Let G be a compact abelian group and let T be the character group of G. Suppose £ is a subset of T. A trigonometric polynomial f on G is said to be an ^-polynomial if its Fourier transform / vanishes off E. The set E is said to be a Sidon set if there is a positive number B such that 2^xeb |/(X)| á-B||/||u for all E-polynomials /; here, ||/||„ = sup{ |/(x)| : xEG}. In this note we shall discuss...
متن کاملA note on weak Sidon sequences
A sequence (ai) of integers is weak Sidon or well-spread if the sums ai + aj , for i < j , are all different. Let f (N) denote the maximum integer n for which there exists a weak Sidon sequence 0 a1< · · ·<an N . Using an idea of Lindström [An inequality for B2-sequences, J. Combin. Theory 6 (1969) 211–212], we offer an alternate proof that f (N)<N1/2 + O(N1/4), an inequality due to Ruzsa [Solv...
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We study finite and infinite Sidon sets in N. The additive energy of two sets is used to obtain new upper bounds for the cardinalities of finite Sidon subsets of some sets as well as to provide short proofs of already known results. We also disprove a conjecture of Lindstrom on the largest Sidon set in [1, N ]× [1, N ] and relate it to a known conjecture of Vinogradov concerning the size of the...
متن کاملGeneralized Sidon sets
We give asymptotic sharp estimates for the cardinality of a set of residue classes with the property that the representation function is bounded by a prescribed number. We then use this to obtain an analogous result for sets of integers, answering an old question of Simon Sidon. © 2010 Elsevier Inc. All rights reserved. MSC: 11B
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ژورنال
عنوان ژورنال: Journal of Fourier Analysis and Applications
سال: 2018
ISSN: 1069-5869,1531-5851
DOI: 10.1007/s00041-018-9604-8