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.
Copyright © 2007 Springer-Verlag.
The definitive version is available at: http://link.springer.com/article/10.1007/BF03321635
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.
Ross, William T. and Matheson, Alec L., "An Observation About Frostman Shifts" (2007). Department of Math & Statistics Faculty Publications. 24.