Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7547977 | Statistics & Probability Letters | 2018 | 15 Pages |
Abstract
The celebrated Fourier inversion formula provides a useful way to re-construct a regular enough, e.g. square-integrable, function via its own Fourier transform. In this article, we give the first probabilistic proof of this classical theorem, even for Euclidean spaces of arbitrary dimension. Particularly, our proof motivates why the one-half weight, for the one-dimensional case in Lemma 1, comes naturally to play due to the inherent spatial symmetry; another similar interpretation can be found in the higher dimensional analogue.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Tak Kwong Wong, Sheung Chi Phillip Yam,