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Angular and Tangential Limits of Blaschke Products and their Successive Derivatives

Published online by Cambridge University Press:  20 November 2018

G. T. Cargo
G. T. Cargo*
Affiliation:
Syracuse University
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In this paper, we shall be concerned with bounded, holomorphic functions of the form

where

(1)

(2)

and

(3)

B(z{an}) is called a Blaschke product, and any sequence {an} which satisfies (2) and (3) is called a Blaschke sequence. For a general discussion of the properties of Blaschke products, see (18, pp. 271-285) or (14, pp. 49-52).

According to a theorem due to Riesz (15), a Blaschke product has radial limits of modulus one almost everywhere on C = {z: |z| = 1}. Moreover, it is common knowledge that, if a Blaschke product has a radial limit at a point, then it also has an angular limit at the point (see 14, p. 19 and 6, p. 457).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 14 , 1962 , pp. 334 - 348
Copyright
Copyright © Canadian Mathematical Society 1962

References

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