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Zero Tracts of Blaschke Products

Published online by Cambridge University Press:  20 November 2018

C. N. Linden  and
H. Somadasa
C. N. Linden
Affiliation:
University College of Swansea, Wales
H. Somadasa
Affiliation:
University College of Swansea, Wales
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Let ﹛an﹜ be a sequence of complex numbers such that

and

Then {an} is called a Blaschke sequence. For each Blaschke sequence {an} a Blaschke product is defined as

Thus a Blaschke product B(z, ﹛an﹜) is a function regular in the open unit disk D = {z: |z| < 1﹜ and having a zero at each point of the sequence ﹛an﹜.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 1072 - 1078
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Dienes, P., The Taylor series (New York, 1957).Google Scholar
2. Frostman, O., Potentiel d'équilibre et capacité des ensembles avec quelques applications à la théorie des fonctions (Lund, 1935).Google Scholar
3. Somadasa, H., Blaschke products with zero tangential limits, J. Lond. Math. Soc, 41 (1965), 293–303.Google Scholar