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On generalized Schwarz-Pick estimates. (English) Zbl 1120.30001

The authors used a Hilbert space method to derive generalized Schwarz-Pick estimates concerning the analytic functions in the unit disk.Generalization to operator-valued functions are also given.

MSC:

30A10 Inequalities in the complex plane
47B32 Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces)
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
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References:

[1] DOI: 10.1112/plms/s2-13.1.1 · JFM 44.0289.01 · doi:10.1112/plms/s2-13.1.1
[2] Bénéteau, Complex Analysis and Dynamical Systems, Contemp. Math. 364 pp 5– (2004) · doi:10.1090/conm/364/06672
[3] Bénéteau, Comput. Methods Funct. Theory 4 pp 1– (2004) · Zbl 1067.30094 · doi:10.1007/BF03321051
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[5] Sarason, Sub-Hardy Hilbert Spaces in the Unit Disk, University of Arkansas Lecture Notes in the Mathematical Sciences 10 (1994) · Zbl 1253.30002
[6] Ruscheweyh, Serdica 11 pp 200– (1985)
[7] de Branges, Perturbation Theory and its Applications in Quantum Mechanics pp 295– (1966)
[8] Landau, Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie (1986) · doi:10.1007/978-3-642-71438-2
[9] DOI: 10.1090/S0002-9939-02-06588-7 · Zbl 1012.30015 · doi:10.1090/S0002-9939-02-06588-7
[10] Kreĭn, Hilbert Space Operators and Operator Algebras pp 353– (1972)
[11] Khavinson, Amer. Math. Soc. Transl. (2) 129 (1986)
[12] de Branges, Square Summable Power Series (1966) · Zbl 0153.39602
[13] MacCluer, Complex Var. Theory Appl. 48 pp 711– (2003) · Zbl 1031.30012 · doi:10.1080/0278107031000154867
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