2019
Том 71
№ 11

All Issues

Sheparovych I. B.

Articles: 2
Brief Communications (Ukrainian)

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

Sheparovych I. B., Vynnyts’kyi B. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 3. - pp. 425-430

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 → ∞.

Article (Ukrainian)

On Interpolation Sequences of One Class of Functions Analytic in the Unit Disk

Sheparovych I. B., Vynnyts’kyi B. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 7. - pp. 879-886

We establish a criterion 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 satisfying the relation $$\left( {\exists {\tau }_{1} \in \left( {0;1} \right)} \right)\;\left( {\exists c_1 >0} \right)\;\left( {\forall z,\left| z \right| < 1} \right):\;\left| {f\left( z \right)} \right| \leqslant \exp \left( {c_1 \gamma ^{{\tau }_{1} } \left( {\frac{{c_1 }}{{1 - \left| z \right|}}} \right)} \right),$$ where γ: [1; +∞) → (0; +∞) is an increasing function such that the function lnγ(t) is convex with respect to lnt on the interval [1; +∞) and lnt = o(lnγ(t)), t → ∞.