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The Nehari-Schwarz lemma and infinitesimal boundary rigidity of bounded holomorphic functions

2022/06/09 by Oliver Roth, Roth, Oliver
Mathematics · #30C80 #32A36 #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2206.04346

openalex publication_date 2022/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We survey a number of recent generalizations and sharpenings of Nehari's extension of Schwarz' lemma for holomorphic self-maps of the unit disk. In particular, we discuss the case of infinitely many critical points and its relation to the zero sets and invariant subspaces for Bergman spaces, as well as the case of equality at the boundary.

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