Abstract
This paper gives a negative answer to a question due to V.M. Adamjan, D.Z. Arov and M.G. Krein, and (what is the same) gives a counterexample to D.Sarason's conjecture* concerning exposed points inH 1.
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References
D. Sarason, “Exposed points inH 1”,Operator theory: Advances and applications,41 (1989) 485–495.
J.B. Garnett,Bounded analytic functions, Academic Press, New York, 1981.
D.Z. Arov, “γ-generating matrices,j-inner matrix-functions and related extrapolation problems”,Teor. Funkt. Anal. i ikh Prilozhen. 51 (1989) 61–67,52 (1989) 57–65,53 (1990) 57–65, Russian. English transl.,J. Sov. Math. 52 (1990) 3487–3491,52 (1990) 3421–3425,58 (1992) 532–537.
N.I. Akhiezer,The classical moment problem and some related question in analysis, Edinburgh, Oliver & Boyd, 1965 (Translation from Russian Edition: Moscow, 1961).
A.Ya. Kheifets, “Nevanlinna- Adamjan- Arov- Krein theorem in semi- determined case”,Teor. Funkt., Funkt. Anal. i ikh Prilozhen. 56 (1991) 128–137, Russian.
A.Ya. Kheifets, “Hanburger moment problem: Parseval equality andA-singularity” (in preperation).
V.M. Adamjan, D.Z. Arov and M.G. Krein, “Infinite Hankel matrices and generalized problems of Carathéodory-Fejér and I. Schur”,Funkt. Anal. i Prilozhen. 2:4 (1968) 1–17, Russian. English transl.,Funct. Anal. Appl. 2 (1968) 269–281.
A.Ya. Kheifets, “Parseval equality in abstract interpolation problem and coupling of open systems”,Teor. Funk., Funk. Anal. i ikh Prilozhen 49 (1988) 112–120,50 (1988) 98–103, Russian. English transl.,J. Sov. Math. 49, 4 (1990) 1114–1120,49, 6 (1990) 1307–1310.
V. Katsnelson, “Continual analogies to the Hamburger-Nevanlinna theorem and the Principal Matrix Enequalities of the classical problems”,Teor. Funk., Funk. Anal. i ikh Prilozhen 36 (1981) 31–48,37 (1982) 31–48,39 (1983) 61–63,40 (1983) 79–90, Russian.
J. Inoue, “An example of non-exposed extremal function in the unit ball ofH 1”,Proceedings of the Edinburgh Mathematical Society.37 (1993) 47–51.