On the equivalence of some conditions for the class of functions analytic in the half-plane

Hishchak Tetyana Ihorivna

Hishchak Tetyana Ihorivna ¹

¹ Department of Mathematics and Economics, Drohobych Ivan Franko state Pedagogical University, Lviv region, Drohobych, 82100, Ukraine

Keywords: class of functions

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Abstract

Let H∞σ(C+) is a space of functions analytic in the half-plane  $\mathbb C_{+}= \{ z: \text {Re} z>0 \}$

supz∈C+{|G(z)|e−σ|Imz|}<+∞.

For this space, the equivalence of a rapid decrease along the positive semi-axis of the modulus of the function is established  $G\in H^{\infty}_{\sigma}(\mathbb C_{+})$

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ACS Style: Hishchak, T.I. On the equivalence of some conditions for the class of functions analytic in the half-plane. Bukovinian Mathematical Journal. 2016, 2
AMA Style: Hishchak TI. On the equivalence of some conditions for the class of functions analytic in the half-plane. Bukovinian Mathematical Journal. 2016; 2(4).
Chicago/Turabian Style: Tetyana Ihorivna Hishchak. 2016. "On the equivalence of some conditions for the class of functions analytic in the half-plane". Bukovinian Mathematical Journal. 2 no. 4.

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