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Fourier transform on integrable Boehmians. (English) Zbl 1191.42003

The authors first establish sufficient conditions for a function to be in \((L^1(\mathbb{R}))^{\wedge}\), the space of the Fourier transforms of integrable functions on \(\mathbb{R}\). Moreover, two characterizations for continuous functions vanishing at \(\infty\) and which belong to \((L^1(\mathbb{R}))^{\wedge}\) are proved and used to give some examples. Finally, they characterize the continuous functions which are Fourier transforms of functions in the Boehmian space introduced by D. Nemzer [Appl. Anal. Discrete Math. 1, 172–183 (2007; Zbl 1199.46096)]. This allows them to answer a question raised by Nemzer in that paper.

MSC:

42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
44A40 Calculus of Mikusiński and other operational calculi

Citations:

Zbl 1199.46096
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References:

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