A notion of extremal analytic discs related to interpolation in the ball
type: Item
instance of: scholarly article
title: A notion of extremal analytic discs related to interpolation in the ball
zbMATH Open document ID: 0808.32001
DOI: 10.1007/BF01450495
author: Eric Amar
author: Pascal J. Thomas
published in: Mathematische Annalen
publication date: 1994-12-11T00:00:00Z
full work available at URL: https://eudml.org/doc/165261
review text: J. Globevnik showed that one can find a proper analytic disc through any discrete subset of the unit ball. We want to characterize those discs such that the preimages in the disc of the points in the ball are in a sense as close together as possible. More precisely, we want the preimage sequence to be the least interpolating possible (in the sense of L. Carleson). Since a sequence in the disc is interpolating iff \(\delta\) is positive, where \(\delta\) is the infimum taken over all base points in the sequence of the product of the invariant (Gleason) distances from that point to all the remaining ones, we are looking for an analytic disc which would minimize \(\delta\) for the preimage sequence. In the case of a finite sequence, we show that -- if such an extremal disc exists, it must be quite regular -- there does exist an extremal disc for a large set of finite sequences -- it can fail to exist even in the case of some sequence of three points, which are characterized explicitly.
Mathematics Subject Classification ID: 32A10
Mathematics Subject Classification ID: 32A17
Mathematics Subject Classification ID: 30E05
Mathematics Subject Classification ID: 30D50
Mathematics Subject Classification ID: 32F45
Mathematics Subject Classification ID: 32H40
zbMATH DE Number: 701007
zbMATH Keywords: extremal analytic discs
zbMATH Keywords: interpolation
zbMATH Keywords: unit ball
MaRDI profile type: Publication
cites work: Q3331503
cites work: Q3715407
cites work: An Interpolation Problem for Bounded Analytic Functions
cites work: Discs in the ball containing given discrete sets
cites work: Q3958740
description: scientific article; zbMATH DE number 701007