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AN ELEMENTARY PROOF OF A SCHWARZ LEMMA FOR THE SYMMETRIZED BIDISC

AN ELEMENTARY PROOF OF A SCHWARZ LEMMA FOR THE SYMMETRIZED BIDISC DEMONSTRATE MATHEMATICAVol. XXXVINo 22003Hidetaka Hamada, Hiroumi SegawaAN ELEMENTARY PROOF OF A SCHWARZ LEMMAFOR THE SYMMETRIZED BIDISCAbstract. Agler-Young obtained a Schwarz lemma for the symmetrized bidisc. Theirproof uses an earlier result of them whose proof is operator-theoretic in nature. They posedthe question to give an elementary proof of the Schwarz lemma for the symmetrized bidisc.In this paper, we give an elementary proof of the Schwarz lemma for the symmetrizedbidisc.1. IntroductionLetr = {(Ai + A 2 , A i A 2 ) : | A i | < l , | A 2 | < l }be the symmetrized bidisc. Agler-Young [2] obtained a Schwarz lemma foranalytic functions ip from the unit disc D to T with y?(0) = (0,0). Theirproof uses a result in Agler-Young [1] whose proof is operator-theoretic innature. However, the nature of the assertion for the Schwarz lemma for thesymmetrized bidisc is purely function-theoretic. So, they posed the questionto give an elementary proof of the Schwarz lemma for the symmetrizedbidisc.In this paper, we will give an elementary proof of the Schwarz lemma forthe symmetrized bidisc.A Schwarz lemma for the symmetrized bidisc throws light on the spectralNevanlinna-Pick problem, which is to interpolate from the unit disc to theset http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

AN ELEMENTARY PROOF OF A SCHWARZ LEMMA FOR THE SYMMETRIZED BIDISC

Demonstratio Mathematica , Volume 36 (2): 6 – Apr 1, 2003

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Publisher
de Gruyter
Copyright
© by Hidetaka Hamada
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2003-0208
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATE MATHEMATICAVol. XXXVINo 22003Hidetaka Hamada, Hiroumi SegawaAN ELEMENTARY PROOF OF A SCHWARZ LEMMAFOR THE SYMMETRIZED BIDISCAbstract. Agler-Young obtained a Schwarz lemma for the symmetrized bidisc. Theirproof uses an earlier result of them whose proof is operator-theoretic in nature. They posedthe question to give an elementary proof of the Schwarz lemma for the symmetrized bidisc.In this paper, we give an elementary proof of the Schwarz lemma for the symmetrizedbidisc.1. IntroductionLetr = {(Ai + A 2 , A i A 2 ) : | A i | < l , | A 2 | < l }be the symmetrized bidisc. Agler-Young [2] obtained a Schwarz lemma foranalytic functions ip from the unit disc D to T with y?(0) = (0,0). Theirproof uses a result in Agler-Young [1] whose proof is operator-theoretic innature. However, the nature of the assertion for the Schwarz lemma for thesymmetrized bidisc is purely function-theoretic. So, they posed the questionto give an elementary proof of the Schwarz lemma for the symmetrizedbidisc.In this paper, we will give an elementary proof of the Schwarz lemma forthe symmetrized bidisc.A Schwarz lemma for the symmetrized bidisc throws light on the spectralNevanlinna-Pick problem, which is to interpolate from the unit disc to theset

Journal

Demonstratio Mathematicade Gruyter

Published: Apr 1, 2003

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