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Bulletin of the London Mathematical Society (1)

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1 results

möbius instability of sampling for small weighted spaces of analytic functions
rémi dhuez
Journal:

Bulletin of the London Mathematical Society / Volume 37 / Issue 5 / October 2005

Published online by Cambridge University Press:

23 September 2005, pp. 738-746

Print publication:

October 2005
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in this paper, the space $\mathcal{a}_\psi(\mathbb{d})$ is considered, consisting of those holomorphic functions $f$ on the unit disk $\mathbb{d}$ such that $\|f\|_\psi=\sup_{z\in\mathbb{d}}|f(z)|\psi(|z|)<+\infty$, with $\psi(1)=0$. the sampling problem is studied for weights satisfying $\ln\psi(r)/\ln(1-r)\to0$. möbius stability of sampling is shown to fail in this space.