Rapidly growing Fourier integrals

Details Rapidly growing Fourier integrals Rapidly growing Fourier integrals

2001-01-02

arxiv.org/abs/math/0101013v1

Mathematics

Classical Analysis and ODEs

Scientific paper

The Riemann-Lebesgue Lemma says that the Fourier transform of an absolutely integrable function on the real line tends to zero as the transform parameter tends to infinity. When the integral is allowed to converge conditionally, the transform can have arbitrarily rapid pointwise growth as the transform parameter tends to infinity. Smoothness of the function to be transformed need not decrease growth of the transform.

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