ON INTERPOLATION SEQUENCES OF ONE CLASS OF FUNCTIONS, ANALYTIC IN THE HALF-PLANE


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Abstract

A new criterion of solvability of the interpolation problem fn)=bn in the class of functions f, analytic in the right half-plane ℂ+ and such that there exists c1∈ 0;+∞ such that |f(z)|≤c1 exp(η(c1|z|)) for all z→ℂ+, where η is a positive increasing continuous differentiable function on [0;+∞), for which η(t)→+∞ as t → +∞ and there exists c2→(0;+∞) such thatfor all t ≥ 1 is described.

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