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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Christian Berg and Antonio J. Duran
Journal: Proc. Amer. Math. Soc. 125 (1997), 523-530
MSC (1991): Primary 42C05, 44A60
MathSciNet review: 1353377
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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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Additional Information

Christian Berg
Affiliation: Matematisk Institut, Københavns Universitet, Universitetsparken 5, DK-2100 Køben- havn Ø, Denmark
Email: berg@math.ku.dk

Antonio J. Duran
Affiliation: Departamento de An\acc alisis Matem\acc atico, Universidad de Sevilla, Apdo. 1160. 41080-Sevilla, Spain
Email: duran@cica.es

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03613-7
PII: S 0002-9939(97)03613-7
Received by editor(s): August 29, 1995
Additional Notes: This work has been partially supported by DGICYT ref. PB93-0926.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society