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- W2000333650 abstract "Let $mathcal {C}(z)$ be the Hilbert space of formal power series in ${z_1}, cdots ,{z_r}(r geqq 1)$. An ideal of $mathcal {C}(z)$ is a vector subspace $mathcal {M}$ of $mathcal {C}(z)$ which contains ${z_1}f(z), cdots ,{z_r}f(z)$ whenever it contains $f(z)$. If $B(z)$ is a formal power series such that $B(z)f(z)$ belongs to $mathcal {C}(z)$ and $||B(z)f(z)|| = ||f(z)||$, then the set $mathcal {M}(B)$ of all products $B(z)f(z)$ is a closed ideal of $mathcal {C}(z)$. In the case $r = 1$, Beurling showed that every closed ideal is of this form for some such $B(z)$. Here we give conditions under which a closed ideal is of the form $mathcal {M}(B)$ for $r geqq 2$." @default.
- W2000333650 created "2016-06-24" @default.
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- W2000333650 date "1973-02-01" @default.
- W2000333650 modified "2023-09-24" @default.
- W2000333650 title "Ideals of square summable power series in several variables" @default.
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- W2000333650 doi "https://doi.org/10.1090/s0002-9939-1973-0312254-4" @default.
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