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

DOI:
https://doi.org/10.1090/S0002-9939-97-03613-7

MathSciNet review:
1353377

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Abstract | References | Similar Articles | Additional Information

Abstract: In this note measures with finite index of determinacy (i.e. determinate measures for which there exists a polynomial such that 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:
https://doi.org/10.1090/S0002-9939-97-03613-7

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