Operator-valued Herglotz kernels and functions of positive real part on the ball

DOI10.1007/s11785-009-0012-6zbMath1206.32002arXiv0801.0438OpenAlexW2081258359MaRDI QIDQ1958688

Michael T. Jury

Publication date: 4 October 2010

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.0438

zbMATH Keywords

\(C^{\ast}\)-algebrapositive real partHerglotz kernelholomorphic functions in the unit balloperator-valued Herglotz formula

Mathematics Subject Classification ID

Spaces of vector- and operator-valued functions (46E40) General theory of (C^*)-algebras (46L05) Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels) (32A26) Holomorphic functions of several complex variables (32A10) Functional analysis techniques applied to functions of several complex variables (32A70)

Related Items (4)

Herglotz functions of several quaternionic variables ⋮ Herglotz functions: the Fueter variables case ⋮ Clark theory in the Drury-Arveson space ⋮ Aleksandrov-Clark theory for Drury-Arveson space

Cites Work

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• Positivity aspects of the Fantappiè transform
• Integral formulas for a sub-Hardy Hilbert space on the ball with complete Nevanlinna–Pick reproducing kernel
• Isometric Dilations for Infinite Sequences of Noncommuting Operators
• Reproducing kernels, de Branges-Rovnyak spaces, and norms of weighted composition operators
• Holomorphic Functions With Positive Real Part on Polycylinders

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