# Exact Kronecker constants of Hadamard sets

Colloquium Mathematicae (2013)

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

top

## Abstract

top
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, $\alpha 1,m,...,{m}^{d-1}=\left({m}^{d-1}-1\right)/\left(2\left({m}^{d}-1\right)\right)$ and α1,m,m²,... = 1/(2m).

## How to cite

top

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 -

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.