Some results on Kronecker, Dirichlet and Helson sets

Thomas-William Korner

Annales de l'institut Fourier (1970)

  • Volume: 20, Issue: 2, page 219-324
  • ISSN: 0373-0956

Abstract

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We construct the following: a perfect non Dirichlet set every proper closed subset of which is Kronecker, A weak Kronecker set which is not an R set; an independent countable Dirichlet set which is not Kronecker; a collection of q -disjoint Kronecker sets whose union is independent but Helson 1 / q ; A countable collection of disjoint Kronecker sets whose union is closed and independent but not Helson: a perfect independent Dirichlet set which is not Helson.

How to cite

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Korner, Thomas-William. "Some results on Kronecker, Dirichlet and Helson sets." Annales de l'institut Fourier 20.2 (1970): 219-324. <http://eudml.org/doc/74016>.

@article{Korner1970,
abstract = {We construct the following: a perfect non Dirichlet set every proper closed subset of which is Kronecker, A weak Kronecker set which is not an $R$ set; an independent countable Dirichlet set which is not Kronecker; a collection of $q$-disjoint Kronecker sets whose union is independent but Helson $1/q$; A countable collection of disjoint Kronecker sets whose union is closed and independent but not Helson: a perfect independent Dirichlet set which is not Helson.},
author = {Korner, Thomas-William},
journal = {Annales de l'institut Fourier},
keywords = {approximation and series expansion},
language = {eng},
number = {2},
pages = {219-324},
publisher = {Association des Annales de l'Institut Fourier},
title = {Some results on Kronecker, Dirichlet and Helson sets},
url = {http://eudml.org/doc/74016},
volume = {20},
year = {1970},
}

TY - JOUR
AU - Korner, Thomas-William
TI - Some results on Kronecker, Dirichlet and Helson sets
JO - Annales de l'institut Fourier
PY - 1970
PB - Association des Annales de l'Institut Fourier
VL - 20
IS - 2
SP - 219
EP - 324
AB - We construct the following: a perfect non Dirichlet set every proper closed subset of which is Kronecker, A weak Kronecker set which is not an $R$ set; an independent countable Dirichlet set which is not Kronecker; a collection of $q$-disjoint Kronecker sets whose union is independent but Helson $1/q$; A countable collection of disjoint Kronecker sets whose union is closed and independent but not Helson: a perfect independent Dirichlet set which is not Helson.
LA - eng
KW - approximation and series expansion
UR - http://eudml.org/doc/74016
ER -

References

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