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Matematicheskie Zametki, 2013, Volume 93, Issue 4, Pages 555–565
DOI: https://doi.org/10.4213/mzm9093 (Mi mzm9093) 		 
On the Representation of Functions as Fourier Integrals

Yu. S. Kolomoitsevab

a Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences
b Donetsk National University
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DOI: https://doi.org/10.4213/mzm9093
Abstract: Sufficient conditions for the representation of functions as the Fourier integral in $\mathbb R^d$ of a function belonging to the space $L_1\cap L_p$, where $0<p<2$, are obtained. The sharpness of these conditions is shown.
Keywords: Fourier integral, Euclidean space $\mathbb R^d$, the space $L_p$, $0<p<2$.
Received: 23.03.2011
English version:
Mathematical Notes, 2013, Volume 93, Issue 4, Pages 561–570
DOI: https://doi.org/10.1134/S0001434613030243
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: Yu. S. Kolomoitsev, “On the Representation of Functions as Fourier Integrals”, Mat. Zametki, 93:4 (2013), 555–565; Math. Notes, 93:4 (2013), 561–570
Citation in format AMSBIB
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