Abstract
A general overview is given for whether a trigonometric series is the Fourier series of an integrable function and when such a series can be approximated in L1 by its partial sums. This is a necessary preliminary for the attempt to generalize the problem of L1 convergence of trigonometric series to the non-periodic case, which is the main instance of the present study.
| Original language | English |
|---|---|
| Title of host publication | Trends in Mathematics |
| Publisher | Springer Science and Business Media Deutschland GmbH |
| Pages | 121-130 |
| Number of pages | 10 |
| DOIs | |
| State | Published - 2024 |
Publication series
| Name | Trends in Mathematics |
|---|---|
| Volume | 7 |
| ISSN (Print) | 2297-0215 |
| ISSN (Electronic) | 2297-024X |
Bibliographical note
Publisher Copyright:© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
Keywords
- Bounded variation
- Fourier transform
- Integrability
- L convergence
- Trigonometric series