Loading...
Please wait, while we are loading the content...
Similar Documents
Almost everywhere convergence of inverse fourier transforms
| Content Provider | Semantic Scholar |
|---|---|
| Author | Colzani, Leonardo Meaney, Christopher A. Prestini, Elena |
| Copyright Year | 2006 |
| Abstract | We show that if log(2 - Delta)f epsilon L-2(R-d), then the inverse Fourier transform of f converges almost everywhere. Here the partial integrals in the Fourier inversion formula come from dilates of a closed bounded neighbourhood of the origin which is star shaped with respect to 0. Our proof is based on a simple application of the Rademacher-Menshov Theorem. In the special case of spherical partial integrals, the theorem was proved by Carbery and Soria. We obtain some partial results when root(log(2 - Delta))f epsilon L-2(R-d) and log log(4 - Delta)f epsilon L-2(R-d). We also consider sequential convergence for general elements of L-2(R-d). |
| Starting Page | 1651 |
| Ending Page | 1660 |
| Page Count | 10 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9939-05-08329-2 |
| Volume Number | 134 |
| Alternate Webpage(s) | http://www.ams.org/journals/proc/2006-134-06/S0002-9939-05-08329-2/S0002-9939-05-08329-2.pdf |
| Alternate Webpage(s) | http://web.science.mq.edu.au/~chrism/ColzaniMeaneyPrestini.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9939-05-08329-2 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
