Abstract
New sufficient conditions for the representation of a function via an absolutely convergent Fourier integral are obtained in the paper. In the main result, this is controlled by the behavior near infinity of both the function and its derivative. This result is extended to any dimension d≥2.
Original language | English |
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Pages (from-to) | 438-459 |
Number of pages | 22 |
Journal | Journal of Approximation Theory |
Volume | 163 |
Issue number | 4 |
DOIs | |
State | Published - Apr 2011 |
Bibliographical note
Funding Information:The work of the second author was also supported by the Ukranian Fund for Fundamental Research Ukraine, Project F25. 1/055.
Funding
The work of the second author was also supported by the Ukranian Fund for Fundamental Research Ukraine, Project F25. 1/055.
Funders | Funder number |
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State Fund for Fundamental Research of Ukraine |
Keywords
- Fourier integral
- Fourier multiplier
- Vitali variation