This article is cited in 10 papers

Division theorem in some weighted spaces of entire functions

A. V. Abanin^ab, D. A. Abanina<sup>ab

a</sup> Southern Federal University, Russia, Rostov-on-Don
^b South Mathematical Institute of VSC RAS, Russia, Vladikavkaz

Abstract: We consider weighted spaces of entire functions which are dual to the Beurling spaces of ultradifferentiable functions of mean type. We prove a division theorem, which completely characterizes all divisors of these spaces. With the help of this theorem, we obtain a criterion for the solvability of convolution equations in the Beurling classes of mean type.

Key words: multiplication operator, division theorem, ultradifferentiable functions, convolution operator.

UDC: 517.547.2+517.982

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