Some problems on optimal approximants

TL;DR

This paper explores various issues related to cyclicity in Dirichlet-type spaces, focusing on polynomials that minimize the norm of the product with a function minus one, highlighting challenges in optimal approximation.

Contribution

It provides an analysis of problems associated with optimal approximants and cyclicity in Dirichlet-type spaces, offering new insights into polynomial minimization challenges.

Findings

Identification of key problems in cyclicity and approximation in Dirichlet spaces

Analysis of polynomial minimization in the context of cyclicity

Discussion of challenges in optimal approximant construction

Abstract

We present an account of different problems that arise in relation with cyclicity problems in Dirichlet-type spaces, in particular with polynomials $p$ that minimize the norm $\|pf-1\|$.