Abstract:
Two types of classes of entire functions (Wα and Zα), which are rapidly decreasing on the real axis are considered. Conditions to ensure that these classes are non-trivial are found and the classes of
the corresponding Fourier transforms are described. Results on the classes Zα are applied to the question of whether a rapidly decreasing function with rapidly decreasing Fourier transform is trivial.
This yields not just an extension of Morgan's well-known theorem, but also its converse.
Bibliography: 18 titles.
Citation:
A. M. Sedletskii, “Classes of entire functions that are rapidly decreasing on the real axis: theory and applications”, Sb. Math., 199:1 (2008), 131–157
\Bibitem{Sed08}
\by A.~M.~Sedletskii
\paper Classes of entire functions that are rapidly decreasing on the real axis: theory and applications
\jour Sb. Math.
\yr 2008
\vol 199
\issue 1
\pages 131--157
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Linking options:
https://www.mathnet.ru/eng/sm3882
https://doi.org/10.1070/SM2008v199n01ABEH003913
https://www.mathnet.ru/eng/sm/v199/i1/p133
This publication is cited in the following 5 articles:
Chiara Amorino, Denis Belomestny, Vytautė Pilipauskaitė, Mark Podolskij, Shi-Yuan Zhou, “Polynomial rates via deconvolution for nonparametric estimation in McKean–Vlasov SDEs”, Probab. Theory Relat. Fields, 2024
Il’d.K.h. Musin, M.I.. Musin, “On a space of entire functions rapidly decreasing on the real axis and its Fourier transform”, European Journal of Mathematics, 2015
M. I. Musin, “O prostranstve tselykh funktsii, bystro ubyvayuschikh na veschestvennoi pryamoi”, Ufimsk. matem. zhurn., 4:1 (2012), 136–145
A. M. Sedletskii, “Rapid Decrease of Entire Functions along the Real Axis and the Uniqueness of the Fourier-Transform Pair”, Math. Notes, 92:2 (2012), 270–279
I.A. Cheltsov, “Extremal metrics on two Fano varieties”, Sb. Math, 200:1 (2009), 95
Citation in format AMSBIB
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