Geodesic
Perturbations of an Integer Sequence as Zero Sets of Divisors
Matematičeskie zametki, Tome 113 (2023) no. 5, pp. 633-645

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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.
Mots-clés : ultradistribution, Fourier–Laplace transform
Keywords: zero set, entire function, division theorem, convolution operator. 
@article{MZM_2023_113_5_a0,
     author = {N. F. Abuzyarova},
     title = {Perturbations of an {Integer} {Sequence} as {Zero} {Sets} of {Divisors}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {633--645},
     publisher = {mathdoc},
     volume = {113},
     number = {5},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_5_a0/}
}
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N. F. Abuzyarova. Perturbations of an Integer Sequence as Zero Sets of Divisors. Matematičeskie zametki, Tome 113 (2023) no. 5, pp. 633-645. http://geodesic.mathdoc.fr/item/MZM_2023_113_5_a0/