Geodesic
On the Growth of Blaschke Products
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 595-601

Voir la notice de l'article provenant de la source Cambridge University Press

It is well known that the distribution of the zeros of an analytic function affects its rate of growth. The literature is too extensive to indicate here. We only point out (1, p. 27; 2; 3; 5), where the angular distribution of the zeros plays a role, as it will in this paper. In private communication, A. Zygmund has raised the following related question, which is the subject of our investigation here.Let {zn }, n = 1, 2, 3, ..., be a sequence of non-zero complex numbers of modulus less than 1, such that ∑(1 – |zn |) < ∞, and consider the Blaschke product 1 Let 2 What are the sequences {zn } for which I(r) is a bounded function of r? 
MacLane, G. R.; Rubel, L. A. On the Growth of Blaschke Products. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 595-601. doi: 10.4153/CJM-1969-067-3
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[1] 1. Boas, R. P., Entire functions (Academic Press, New York, 1954). Google Scholar

[2] 2. Linden, C. N., The distribution of the zeros of regular functions, Proc. London Math. Soc. (3) 15 (1965), 301–322. Google Scholar

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[4] 4. Rubel, L. A., A Fourier series method for entire functions, Duke Math. J. 30 (1963), 437–442. Google Scholar

[5] 5. Rubel, L. A. and Taylor, B. A., A Fourier series method for meromorphic and entire functions, Bull. Soc. Math. France 96 (1968), 53–96. Google Scholar

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