On the Berg–Chen–Ismail theorem and the Nevanlinna–Pick problem

L. Golinskii^a, F. Peherstorfer^b, P. Yuditskii<sup>b

a</sup> Mathematical Division, B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv, 61103, Ukraine
^b Institute for Analysis, Johannes Kepler University Linz, A-4040 Linz, Austria

Abstract: In 2002, C. Berg, Y. Chen, and M. Ismail found a nice relation between the determinacy of the Hamburger moment problem and asymptotic behavior of the smallest eigenvalues of the corresponding Hankel matrices. We investigate whether an analog of this statement holds for the Nevanlinna–Pick interpolation problem.

Key words and phrases: moment problem, Blaschke product, Carleson measure, Pick matrix.

MSC: 30E05 (primary), 30D50 (secondary)

Received: 19.05.2008

Language: English

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