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Some Lemmas on Interpolating Blaschke Products and a Correction

Published online by Cambridge University Press:  20 November 2018

A. Kerr-Lawson
A. Kerr-Lawson*
Affiliation:
University of Waterloo, Waterloo, Ontario
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A Blaschke product on the unit disc,

where |c|= 1 and kis a non-negative integer, is said to be interpolatingif the condition

C

is satisfied for a constant δ independent of m.A Blaschke product always belongs to the set I of inner functions; it has norm 1 and radial limits of modulus 1 almost everywhere. The most general inner function can be uniquely factored into a product BS,where Bis a Blaschke product and

for some positive singular measure μ(θ) on the unit circle. The discussion will be carried out in terms of the hyperbolic geometry on the open unit disc D,its metric

and its neighbourhoods N(x, ∈) = ﹛z′ ∈ D: Ψ(z, z′) < ∈ ﹜

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 531 - 534
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Hoffman, K., Banach spaces of analytic functions (Prentice-Hall, Englewood Cliffs, N.J., 1962).Google Scholar
2. Kerr-Lawson, A., A filter description of the homomorphisms of H00, Can. J. Math. 17 (1965), 734–757.Google Scholar
3. Nehari, Z., Conformai mapping (McGraw-Hill, New York, 1952).Google Scholar