Rapidly growing Fourier integrals

Erik Talvila

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arXiv · math/0101013

Rapidly growing Fourier integrals

Erik Talvila

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Abstract

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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Erik Talvila. 2001-01-02. Rapidly growing Fourier integrals. https://arxiv.org/abs/math/0101013

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