# 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

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topBennett, 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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