A classical theorem of Frostman says that if B is a Blaschke product (or any inner function), then its Frostman shifts Bw = (B w)(1 w­­¯B)1 are Blaschke products for all |w| < 1 except possibly for w in a set of logarithmic capacity zero. If B is a Frostman Blaschke product, equivalently an inner multiplier for the space of Cauchy transforms of measures on the unit circle, we show that for all |w| < 1, Bw is indeed another Frostman Blaschke product.

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Copyright © 2007 Springer-Verlag.

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DOI: 10.1007/BF03321635

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Matheson, Alec L., and William T. Ross. "An Observation about Frostman Shifts." Computational Methods and Function Theory 7, no. 1 (2007): 111-126. doi:10.1007/BF03321635.

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