The divergence of Mock Fourier series for spectral measures
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914563726770176 |
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| author | Pan, Wu-Yi Ai, Wen-Hui |
| author_facet | Pan, Wu-Yi Ai, Wen-Hui |
| contents | In this paper, we study divergence properties of Fourier series on Cantor-type fractal measure, also called Mock Fourier series. We give a sufficient condition under which the Mock Fourier series for doubling spectral measure is divergent on non-zero set. In particularly, there exists an example of the quarter Cantor measure whose Mock Fourier sums is not almost everywhere convergent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_01124 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The divergence of Mock Fourier series for spectral measures Pan, Wu-Yi Ai, Wen-Hui Functional Analysis 28A80, 42A20, 42B05 In this paper, we study divergence properties of Fourier series on Cantor-type fractal measure, also called Mock Fourier series. We give a sufficient condition under which the Mock Fourier series for doubling spectral measure is divergent on non-zero set. In particularly, there exists an example of the quarter Cantor measure whose Mock Fourier sums is not almost everywhere convergent. |
| title | The divergence of Mock Fourier series for spectral measures |
| topic | Functional Analysis 28A80, 42A20, 42B05 |
| url | https://arxiv.org/abs/2206.01124 |