On interpolation by functions in ℓ_{𝐴}^{𝑝}

Abstract

This work explores several aspects of interpolating sequences for ℓ A p \ell ^p_A , the space of analytic functions on the unit disk with p 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.