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Search: MSC category 46J15 ( Banach algebras of differentiable or analytic functions, $H^p$-spaces [See also 30H10, 32A35, 32A37, 32A38, 42B30] )

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1. CMB 2015 (vol 58 pp. 350)

Merino-Cruz, Héctor; Wawrzynczyk, Antoni
 On Closed Ideals in a Certain Class of Algebras of Holomorphic Functions We recently introduced a weighted Banach algebra $\mathfrak{A}_G^n$ of functions which are holomorphic on the unit disc $\mathbb{D}$, continuous up to the boundary and of the class $C^{(n)}$ at all points where the function $G$ does not vanish. Here, $G$ refers to a function of the disc algebra without zeros on $\mathbb{D}$. Then we proved that all closed ideals in $\mathfrak{A}_G^n$ with at most countable hull are standard. In the present paper, on the assumption that $G$ is an outer function in $C^{(n)}(\overline{\mathbb{D}})$ having infinite roots in $\mathfrak{A}_G^n$ and countable zero set $h(G)$, we show that all the closed ideals $I$ with hull containing $h(G)$ are standard. Keywords:Banach algebra, disc algebra, holomorphic spaces, standard idealCategories:46J15, 46J20, 30H50

2. CMB 2011 (vol 54 pp. 338)

Nakazi, Takahiko
 SzegÃ¶'s Theorem and Uniform Algebras We study SzegÃ¶'s theorem for a uniform algebra. In particular, we do it for the disc algebra or the bidisc algebra. Keywords:SzegÃ¶'s theorem, uniform algebras, disc algebra, weighted Bergman spaceCategories:32A35, 46J15, 60G25

3. CMB 2008 (vol 51 pp. 378)

Izuchi, Kou Hei
 Cyclic Vectors in Some Weighted $L^p$ Spaces of Entire Functions In this paper, we generalize a result recently obtained by the author. We characterize the cyclic vectors in $\Lp$. Let $f\in\Lp$ and $f\poly$ be contained in the space. We show that $f$ is non-vanishing if and only if $f$ is cyclic. Keywords:weighted $L^p$ spaces of entire functions, cyclic vectorsCategories:47A16, 46J15, 46H25
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