Homogeneous algebras on the circle. I. Ideals of analytic functions

Colin Bennett; John E. Gilbert

Annales de l'institut Fourier (1972)

  • Volume: 22, Issue: 3, page 1-19
  • ISSN: 0373-0956

Abstract

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Let 𝒜 be a homogeneous algebra on the circle and 𝒜 + the closed subalgebra of 𝒜 of functions having analytic extensions into the unit disk D . This paper considers the structure of closed ideals of 𝒜 + under suitable restrictions on the synthesis properties of 𝒜 . In particular, completely characterized are the closed ideals in 𝒜 + whose zero sets meet the circle in a countable set of points. These results contain some previous results of Kahane and Taylor-Williams obtained independently.

How to cite

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Bennett, Colin, and Gilbert, John E.. "Homogeneous algebras on the circle. I. Ideals of analytic functions." Annales de l'institut Fourier 22.3 (1972): 1-19. <http://eudml.org/doc/74088>.

@article{Bennett1972,
abstract = {Let $\{\cal A\}$ be a homogeneous algebra on the circle and $\{\cal A\}^+$ the closed subalgebra of $\{\cal A\}$ of functions having analytic extensions into the unit disk $D$. This paper considers the structure of closed ideals of $\{\cal A\}^+$ under suitable restrictions on the synthesis properties of $\{\cal A\}$. In particular, completely characterized are the closed ideals in $\{\cal A\}^+$ whose zero sets meet the circle in a countable set of points. These results contain some previous results of Kahane and Taylor-Williams obtained independently.},
author = {Bennett, Colin, Gilbert, John E.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3},
pages = {1-19},
publisher = {Association des Annales de l'Institut Fourier},
title = {Homogeneous algebras on the circle. I. Ideals of analytic functions},
url = {http://eudml.org/doc/74088},
volume = {22},
year = {1972},
}

TY - JOUR
AU - Bennett, Colin
AU - Gilbert, John E.
TI - Homogeneous algebras on the circle. I. Ideals of analytic functions
JO - Annales de l'institut Fourier
PY - 1972
PB - Association des Annales de l'Institut Fourier
VL - 22
IS - 3
SP - 1
EP - 19
AB - Let ${\cal A}$ be a homogeneous algebra on the circle and ${\cal A}^+$ the closed subalgebra of ${\cal A}$ of functions having analytic extensions into the unit disk $D$. This paper considers the structure of closed ideals of ${\cal A}^+$ under suitable restrictions on the synthesis properties of ${\cal A}$. In particular, completely characterized are the closed ideals in ${\cal A}^+$ whose zero sets meet the circle in a countable set of points. These results contain some previous results of Kahane and Taylor-Williams obtained independently.
LA - eng
UR - http://eudml.org/doc/74088
ER -

References

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  14. [14] K. de LEEUW, Homogeneous algebras on compact abelian groups, Trans. Amer. Math. Soc., 87 (1958), 372-386. Zbl0083.34603MR21 #820
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  16. [16] B. NYMAN, On the one-dimensional translation group and semi-group in certain function spaces, Thesis (1950), Uppsala. Zbl0037.35401MR12,108g
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  19. [19] B.A. TAYLOR and D.L. WILLIAMS, The space of functions analytic in the disk with indefinitely differentiable boundary values, (submitted for publication). 

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