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arXiv · 1404.1594

Berger measure for some transformations of subnormal weighted shifts

Raul E. Curto·George R. Exner
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Abstract

A subnormal weighted shift may be transformed to another shift in various ways, such as taking the p-th power of each weight or forming the Aluthge transform. \ We determine in a number of cases whether the resulting shift is subnormal, and, if it is, find a concrete representation of the associated Berger measure, directly for finitely atomic measures, and using both Laplace transform and Fourier transform methods for more complicated measures. \ Alternatively, the problem may be viewed in purely measure-theoretic terms as the attempt to solve moment matching equations such as $(\int t^n \, d\mu(t))^2 = \int t^n \, d\nu(t)$ ($n=0, 1, \ldots$) for one measure given the other.

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BibTeXRIS

Raul E. Curto, George R. Exner. 2014-04-06. Berger measure for some transformations of subnormal weighted shifts. https://doi.org/10.1007/s00020-015-2264-z

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