Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  377.30023
Autor:  Bonar, D.D.; Carroll, F.W.; Erdös, Paul
Title:  Strongly annular functions with small coefficients, and related results. (In English)
Source:  Proc. Am. Math. Soc. 67, 129-132 (1977).
Review:  An analytic function f(z) in the unit disc D = {z: |z| < 1} is called an annular function if there exists a sequence of Jordan curves {Jn} in D such that the origin is in the interior of Jn for each n and

limn ––> oomax{|f(z)|: z in Jn} = oo.

If, in addition, the curves Jn are all circles with center at the origin, then the function f(z) is said to be strongly annular. The authors construct an example of a strongly annular function f(z) = sumn = 0ooanzn such that limn ––> ooan = 0. The construction is very short and elementary. Additional examples of annular functions are presented in which various length and distance apart conditions are placed on the curves Jn. These additional examples involve approximation techniques.
Reviewer:  P.Lappan
Classif.:  * 30D40 Cluster sets, etc.
                   30B10 Power series (one complex variable)

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