Berger measure for some transformations of subnormal weighted shifts

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 $(\int t^{n}d\mu (t){)}^2=\int t^{n}d\nu (t)$ ($n=0,1,\dots$) for one measure given the other.

References in corpus (1)

• On the $\varkappa$th root of a Stieltjes moment sequence

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• Polynomial embeddings of unilateral weighted shifts into $2$-variable weighted shifts
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• The Square Root Problem and Subnormal Aluthge Transforms of Recursively Generated Weighted Shifts