2019
Том 71
№ 8

All Issues

Generalization of the fricke theorem on entire functions of finite index

Sheremeta M. M.

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Abstract

We prove that, for every sequence (a k) of complex numbers satisfying the conditions Σ(1/|a k |) < ∞ and |a k+1| − |a k | ↗ ∞ (k → ∞), there exists a continuous functionl decreasing to 0 on [0, + ∞] and such that f(z) = Π(1 −z/|a k |) is an entire function of finite l-index.

English version (Springer): Ukrainian Mathematical Journal 48 (1996), no. 3, pp 460-466.

Citation Example: Sheremeta M. M. Generalization of the fricke theorem on entire functions of finite index // Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 412-417.

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