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An Observation About Frostman Shifts, William T. Ross, Alec L. Matheson
An Observation About Frostman Shifts, William T. Ross, Alec L. Matheson
Department of Math & Statistics Faculty Publications
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.