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arXiv · 0905.4786

On absolute convergence of Fourier integrals

E. Liflyand·R. Trigub
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Abstract

New sufficient conditions for representation of a function via the absolutely convergent Fourier integral are obtained in the paper. In the main result, Theorem 1.1, this is controlled by the behavior near infinity of both the function and its derivative. This result is extended to any dimension $d\ge2.$

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E. Liflyand, R. Trigub. 2009-05-29. On absolute convergence of Fourier integrals. https://arxiv.org/abs/0905.4786

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