Loewner’s theorem for kernels having a finite number of negative squares

Alpay, D.; Rovnyak, J.

doi:10.1090/S0002-9939-99-04618-3

Loewner’s theorem for kernels having a finite number of negative squares
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by D. Alpay and J. Rovnyak PDF

Proc. Amer. Math. Soc. 127 (1999), 1109-1117 Request permission

Abstract:

By a theorem of Loewner, a continuously differentiable real-valued function on a real interval whose difference quotient is a nonnegative kernel is the restriction of a holomorphic function which has nonnegative imaginary part in the upper half-plane and is holomorphic across the interval. An analogous result is obtained when the difference-quotient kernel has a finite number of negative squares.

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