Exact Kronecker constants of Hadamard sets

• Autorzy: Kathryn E. Hare , L. Thomas Ramsey
• Języki publikacji: EN

Abstrakty

EN

A set S of integers is called ε-Kronecker if every function on S of modulus one can be approximated uniformly to within ε by a character. The least such ε is called the ε-Kronecker constant, κ(S). The angular Kronecker constant is the unique real number α(S) ∈ [0,1/2] such that κ(S) = |exp(2πiα(S)) - 1|. We show that for integers m > 1 and d ≥ 1,
$α{1,m,...,m^{d-1}} = (m^{d-1}-1)/(2(m^{d}-1))$ and α{1,m,m²,...} = 1/(2m).

Kategorie tematyczne

• 65T40: Trigonometric approximation and interpolation
• 42A15: Trigonometric interpolation
• 43A46: Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 130
• Numer: 1
• Strony: 39-49

Daty

wydano

2013

Twórcy

autor

Kathryn E. Hare

• Department of Pure Mathematics, University of Waterloo, Waterloo, Ont., Canada, N2L 3G1

autor

L. Thomas Ramsey

• Department of Mathematics, University of Hawaii at Manoa, Honolulu, HI 96822, U.S.A.

Identyfikatory

DOI

10.4064/cm130-1-4