Monotone operator functions on arbitrary sets

Donoghue, William F.

doi:10.1090/S0002-9939-1980-0548091-9

Monotone operator functions on arbitrary sets
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by William F. Donoghue

Proc. Amer. Math. Soc. 78 (1980), 93-96

DOI: https://doi.org/10.1090/S0002-9939-1980-0548091-9

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Abstract:

We give a new proof of a result of Chandler which shows that a monotone operator function defined on a set J admits an analytic continuation to the upper and lower half-planes, and that this continuation is a Pick function, real and regular on the convex hull of J.

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