2017
Том 69
№ 5

All Issues

Interpolation Sequences for the Class of Functions of Finite η-Type Analytic in the Unit Disk

Sheparovych I. B., Vynnyts’kyi B. V.

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Abstract

We establish conditions for the existence of a solution of the interpolation problem f n ) = b n in the class of functions f analytic in the unit disk and such that $$\left( {\exists \;c_1 > 0} \right)\;\left( {\forall z,\;|\;z\;| < 1} \right):\;\;\left| {f\left( z \right)} \right|\;\; \leqslant \;\;\;\exp \left( {c_1 \eta \left( {\frac{{c_1 }}{{1 - \left| z \right|}}} \right)} \right).$$ Here, η : [1; +∞) → (0; +∞) is an increasing function convex with respect to ln t on the interval [1; +∞) and such that ln t = o(η(t)), t → ∞.

English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 3, pp 520-526.

Citation Example: Sheparovych I. B., Vynnyts’kyi B. V. Interpolation Sequences for the Class of Functions of Finite η-Type Analytic in the Unit Disk // Ukr. Mat. Zh. - 2004. - 56, № 3. - pp. 425-430.

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