Exact Kronecker constants of Hadamard sets

Kathryn E. Hare, and L. Thomas Ramsey. "Exact Kronecker constants of Hadamard sets." Colloquium Mathematicae 130.1 (2013): 39-49. <http://eudml.org/doc/283752>.

@article{KathrynE2013,
abstract = {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 α1,m,m²,... = 1/(2m).},
author = {Kathryn E. Hare, L. Thomas Ramsey},
journal = {Colloquium Mathematicae},
keywords = {Hadamard set; interpolation of trigonometric polynomials; Kronecker constant; Kronecker set; trigonometric approximation},
language = {eng},
number = {1},
pages = {39-49},
title = {Exact Kronecker constants of Hadamard sets},
url = {http://eudml.org/doc/283752},
volume = {130},
year = {2013},
}

TY - JOUR
AU - Kathryn E. Hare
AU - L. Thomas Ramsey
TI - Exact Kronecker constants of Hadamard sets
JO - Colloquium Mathematicae
PY - 2013
VL - 130
IS - 1
SP - 39
EP - 49
AB - 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 α1,m,m²,... = 1/(2m).
LA - eng
KW - Hadamard set; interpolation of trigonometric polynomials; Kronecker constant; Kronecker set; trigonometric approximation
UR - http://eudml.org/doc/283752
ER -