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.
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References
ARONSZAJN, N.: Theorey of reproducing kernels, Tans. Amer. Math. Soc. 68 (1950), 337–404.
BURBEA, J.: Pick's theorem with operator-valued holomorphic functions, Kōdal Math. J. 4 (1981), 495–507.
BURBEA, J.: Operator-valued Pick's conditions and holomorphicity, Pacific J. Math. 98 (1982), 295–311.
DONOGHUE, W.F.: Monotone Matrix Functions and Analytic Continuation, Springer-Verlag, New York, 1974.
FITZGERALD, C.H., and HORN, R.A.: On quadratic and bilinear forms in function theory, Proc. London Math. Soc. (3) 44 (1982), 554–576.
HINDMARSH, A.C.: Pick's conditions and analyticity, Pacific J. Math. 27 (1968), 527–531.
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© 1983 Springer-Verlag Berlin Heidelberg
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Burbea, J. (1983). Positive definiteness and holomorphy. In: Ławrynowicz, J. (eds) Analytic Functions Błażejewko 1982. Lecture Notes in Mathematics, vol 1039. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073356
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DOI: https://doi.org/10.1007/BFb0073356
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