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On Fourier transformation of a class of entire functions
I. Kh. Musina, M. I. Musinb a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, Russia
b Bashkir State University, Ufa, Russia
Abstract:
We consider a space of entire functions of several complex variables decaying fast on Rn and such that their growth along iRn is majorized by means of a family of weight functions. Under certain assumptions for the weight functions we obtain an equivalent description of this space in terms of estimates for partial derivatives of the functions in Rn and prove a Paley–Wiener type theorem.
Keywords:
Gelfand–Shilov spaces, Fourier transform, entire functions, convex functions.
Received: 05.11.2014
Citation:
I. Kh. Musin, M. I. Musin, “On Fourier transformation of a class of entire functions”, Ufa Math. J., 6:4 (2014), 108–121
Linking options:
https://www.mathnet.ru/eng/ufa264https://doi.org/10.13108/2014-6-4-108 https://www.mathnet.ru/eng/ufa/v6/i4/p111
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Abstract page: | 372 | Russian version PDF: | 173 | English version PDF: | 36 | References: | 71 |
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