Abstract
An old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series is extended to the non-periodic case (Fourier transforms). Necessary and sufficient conditions are given as relations between the Fourier transforms and their Hilbert transforms. Sufficient conditions for integrability of the Hilbert transform are obtained.
| Original language | English |
|---|---|
| Pages (from-to) | 934-946 |
| Number of pages | 13 |
| Journal | Journal of Fourier Analysis and Applications |
| Volume | 20 |
| Issue number | 5 |
| DOIs | |
| State | Published - Oct 2014 |
Bibliographical note
Publisher Copyright:© 2014, Springer Science+Business Media New York.
Keywords
- Fourier transform
- Hardy space
- Hilbert transform
- Integrability