Measures with finite index of determinacy or a mathematical model for Dr. Jekyll and Mr. Hyde

Berg, Christian; Duran, Antonio

doi:10.1090/S0002-9939-97-03613-7

Measures with finite index of determinacy or a mathematical model for Dr. Jekyll and Mr. Hyde
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by Christian Berg and Antonio J. Duran PDF

Proc. Amer. Math. Soc. 125 (1997), 523-530 Request permission

Abstract:

In this note measures with finite index of determinacy (i.e. determinate measures $\mu$ for which there exists a polynomial $p$ such that $\vert p\vert ^{2} \mu$ is indeterminate) are characterizated in terms of the operator associated to its Jacobi matrix. Using this characterization, we show that such determinate measures with finite index of determinacy (Jekyll) turn out to be indeterminate (Hyde) when considered as matrices of measures.

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