Perturbations of an Integer Sequence as Zero Sets of Divisors

N. F. Abuzyarova

Matematičeskie zametki, Tome 113 (2023) no. 5, pp. 633-645.

Résumé

We consider weighted spaces of entire functions obtained as the images of spaces of ultradistributions of minimal type and normal type on the real line under the Fourier–Laplace transform. The divisors of these spaces are studied. Namely, we find conditions on a perturbing sequence under which the sequence of integers perturbed by it will be the zero set of an entire function that is a divisor of one of the above-mentioned spaces.

Détail

Mots-clés : ultradistribution, Fourier–Laplace transform
Keywords: zero set, entire function, division theorem, convolution operator.

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