Mathematics Commons^™

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 B_w = (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, B_w is indeed another Frostman Blaschke product.