Pick's theorem with operator-valued holomorphic functions

DOI10.2996/KMJ/1138036431zbMath0478.32020OpenAlexW2072524423MaRDI QIDQ1161071

Jacob Burbea

Publication date: 1981

Published in: Kodai Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2996/kmj/1138036431

zbMATH Keywords

weighted Bergman kernelPick's theoremholomorphic reproducing kernels with contraction-propertypositive-definite sesqui-holomorphic kernelSzegoe Kernel

Mathematics Subject Classification ID

Spaces of vector- and operator-valued functions (46E40) (H^p)-spaces, Nevanlinna spaces of functions in several complex variables (32A35) Hilbert spaces of continuous, differentiable or analytic functions (46E20) Other generalizations of function theory of one complex variable (32A30) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25) Kernel functions in one complex variable and applications (30C40)

Related Items (2)

Positive-Definiteness and its Applications to Interpolation Problems for Holomorphic Functions ⋮ Lower order positivity and holomorphic operators

Cites Work

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• A generalization of Pick's theorem and its applications to intrinsic metrics
• On a metric induced by analytic capacity. II.
• The Caratheodory Metric and its Majorant Metrics
• The kernel functions of Szegö type on Riemann surfaces
• The Rudin kernel and the extremal functions in Hardy classes
• On a metric induced by analytic capacity. I.

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