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Positive definiteness and holomorphy

  • Jacob Burbea
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1039)

Abstract

Conditions for holomorphic extensions of operator-valued functions in domains D (or complex manifolds) of ℂn are formulated in terms of positive-definiteness of order 3 of certain kernels on D×D.

Keywords

Positive Definiteness Riemann Mapping Accretive Operator Holomorphic Extension Hyperbolic Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    ARONSZAJN, N.: Theorey of reproducing kernels, Tans. Amer. Math. Soc. 68 (1950), 337–404.MathSciNetzbMATHCrossRefGoogle Scholar
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    BURBEA, J.: Pick's theorem with operator-valued holomorphic functions, Kōdal Math. J. 4 (1981), 495–507.MathSciNetzbMATHGoogle Scholar
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    BURBEA, J.: Operator-valued Pick's conditions and holomorphicity, Pacific J. Math. 98 (1982), 295–311.MathSciNetzbMATHCrossRefGoogle Scholar
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    DONOGHUE, W.F.: Monotone Matrix Functions and Analytic Continuation, Springer-Verlag, New York, 1974.zbMATHCrossRefGoogle Scholar
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    FITZGERALD, C.H., and HORN, R.A.: On quadratic and bilinear forms in function theory, Proc. London Math. Soc. (3) 44 (1982), 554–576.MathSciNetzbMATHCrossRefGoogle Scholar
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    HINDMARSH, A.C.: Pick's conditions and analyticity, Pacific J. Math. 27 (1968), 527–531.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Jacob Burbea
    • 1
  1. 1.Department of MathematicsUniversity of PittsburghPittsburghUSA

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