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

E. R. Liflyand; R. M. Trigub

doi:10.1134/s0081543810020136

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

E. R. Liflyand, R. M. Trigub

Department of Mathematics

Donetsk National University

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	146-159
Number of pages	14
Journal	Proceedings of the Steklov Institute of Mathematics
Volume	269
Issue number	1
DOIs	https://doi.org/10.1134/s0081543810020136
State	Published - 2010

Bibliographical note

Funding Information:
The second author was supported by the Fundamental Researches State Fund of Ukraine, project no. F25.1/055.

Funding

The second author was supported by the Fundamental Researches State Fund of Ukraine, project no. F25.1/055.

Funders	Funder number
State Fund for Fundamental Research of Ukraine

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10.1134/s0081543810020136

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

Abstract

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