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arXiv · 2210.05823

On Interpolation by Functions in $\ell^p_A$

Raymond Cheng·Christopher Felder
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Abstract

This work explores several aspects of interpolating sequences for $\ell^p_A$, the space of analytic functions on the unit disk with $p$-summable Maclaurin coefficients. Much of this work is communicated through a Carlesonian lens. We investigate various analogues of Gramian matrices, for which we show boundedness conditions are necessary and sufficient for interpolation, including a characterization of universal interpolating sequences in terms of Riesz systems. We also discuss weak separation, giving a characterization of such sequences using a generalization of the pseudohyperbolic metric. Lastly, we consider Carleson measures and embeddings.

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BibTeXRIS

Raymond Cheng, Christopher Felder. 2022-10-11. On Interpolation by Functions in $\ell^p_A$. https://arxiv.org/abs/2210.05823

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