Computational Methods and Function Theory 7 (2007), No. 1, 111--126
Copyright Heldermann Verlag 2007
Alec L. Matheson†
Lamar University, Department of Mathematics, Beaumont, Texas 77710, U.S.A.
William T. Ross
wross@richmond.edu , University of Richmond, Department of Mathematics and Computer Science, Richmond, Virginia 23173, U.S.A.
A classical theorem of Frostman says that if $B$ is a Blaschke product (or any inner function), then its Frostman shifts ${B_w = (B - w)(1 - \overline{w} B)^{-1}}$ 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.
Keywords: Blaschke product, Frostman shifts, multipliers.
MSC 2000: 30E20, 30D50.
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