# Exact Kronecker constants of Hadamard sets

Kathryn E. Hare; L. Thomas Ramsey

Colloquium Mathematicae (2013)

- Volume: 130, Issue: 1, page 39-49
- ISSN: 0010-1354

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topKathryn 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 -

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