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.References
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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 Análisis Matemático, Universidad de Sevilla, Apdo. 1160. 41080-Sevilla, Spain
- Email: duran@cica.es
- 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
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 523-530
- MSC (1991): Primary 42C05, 44A60
- DOI: https://doi.org/10.1090/S0002-9939-97-03613-7
- MathSciNet review: 1353377