• Extremal functions of the Neva...

Treffer: Extremal functions of the Nevanlinna-Pick problem and Douglas algebras

Title:
Extremal functions of the Nevanlinna-Pick problem and Douglas algebras
Authors:
V. Tolokonnikov
Source:
Studia Mathematica. 105:151-158
Publisher Information:
Institute of Mathematics, Polish Academy of Sciences, 1993.
Publication Year:
1993
Subject Terms:
Banach algebras of differentiable or analytic functions, \(H^p\)-spaces, Spaces of bounded analytic functions of one complex variable, Projective and free modules and ideals in commutative rings, 0101 mathematics, Nevanlinna-Pick problem, 01 natural sciences
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Language:
English
ISSN:
1730-6337
0039-3223
DOI:
10.4064/sm-105-2-151-158
Access URL:
https://www.impan.pl/shop/publication/transaction/download/product/108077?download.pdf
https://zbmath.org/714184
https://doi.org/10.4064/sm-105-2-151-158
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-smv105i2p151bwm
Accession Number:
edsair.doi.dedup.....b3fbcfa99a7b1288d7ec8cdc483d9a5c
Database:
OpenAIRE

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Summary: The Nevanlinna-Pick problem at the zeros of a Blaschke product \(B\) having a solution of norm smaller than one is studied. All its extremal solutions are invertible in the Douglas algebra \(D\) generated by \(B\). If \(B\) is a finite product of sparse Blaschke products (Newman-Blaschke products, Frostman-Blaschke products) then so are all the extremal solutions. For a Blaschke product \(B\) a formula given for the number \(C(B)\) such that if the NP-problem has a solution of norm smaller than \(C(B)\) then all its extremal solutions are Carleson-Blaschke products, i.e. can be represented as finite products of interpolating Blaschke products.