Rapidly growing Fourier integrals
经典分析与常微分方程
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0101013,
title = {Rapidly growing Fourier integrals},
author = {Erik Talvila},
journal= {arXiv preprint arXiv:math/0101013},
year = {2007}
}