This article is cited in 5 papers

On the representation of a function as an absolutely convergent Fourier integral

E. R. Liflyand^a, R. M. Trigub<sup>b

a</sup> Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel
^b Faculty of Mathematics, Donetsk National University, Donetsk, Ukraine

Abstract: We obtain new sufficient conditions for the representability of a function by an absolutely convergent Fourier integral in $\mathbb R^d$. These conditions are given in terms of the simultaneous behavior of a function and its derivatives at $\infty$. We test the sharpness of the conditions using well-known examples.

UDC: 517.518.5

Received in November 2009

 English version: Proceedings of the Steklov Institute of Mathematics, 2010, 269, 146–159

Bibliographic databases:

• 
• 
• 
• 
•