# Stable division and essential normality: the non-homogeneous and quasi homogeneous cases

@article{Biswas2015StableDA,
title={Stable division and essential normality: the non-homogeneous and quasi homogeneous cases},
author={S. Biswas and O. Shalit},
journal={arXiv: Functional Analysis},
year={2015}
}
• Published 2015
• Mathematics
• arXiv: Functional Analysis
• Let $\mathcal{H}_d^{(t)}$ ($t \geq -d$, $t>-3$) be the reproducing kernel Hilbert space on the unit ball $\mathbb{B}_d$ with kernel $k(z,w) = \frac{1}{(1-\langle z, w \rangle)^{d+t+1}} .$ We prove that if an ideal $I \triangleleft \mathbb{C}[z_1, \ldots, z_d]$ (not necessarily homogeneous) has what we call the "approximate stable division property", then the closure of $I$ in $\mathcal{H}_d^{(t)}$ is $p$-essentially normal for all $p>d$. We then show that all quasi homogeneous ideals in two… CONTINUE READING
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