DOI

10.1007/s13324-021-00604-2

Abstract

The classical theorems of Mittag-Leffler and Weierstrass show that when (λn)n≥1 is

a sequence of distinct points in the open unit disk D, with no accumulation points in

D, and (wn)n≥1 is any sequence of complex numbers, there is an analytic function

ϕ on D for which ϕ(λn) = wn. A celebrated theorem of Carleson [2] characterizes

when, for a bounded sequence (wn)n≥1, this interpolating problem can be solved with

a bounded analytic function. A theorem of Earl [5] goes further and shows that when

Carleson’s condition is satisfied, the interpolating function ϕ can be a constant multiple

of a Blaschke product. Results from [4] determine when the interpolating function ϕ

can be taken to be zero free. In this paper we explore when ϕ can be an outer function.

Document Type

Article

Publication Date

9-24-2021

Publisher Statement

Copyright © 2021, Springer Link.

DOI: 10.1007/s13324-021-00604-2

The definitive version is available at: https://link.springer.com/article/10.1007/s13324-021-00604-2

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