On absolute convergence of Fourier integrals

Details On absolute convergence of Fourier integrals On absolute convergence of Fourier integrals

2009-05-29

arxiv.org/abs/0905.4786v1

Mathematics

Classical Analysis and ODEs

34 pages

Scientific paper

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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