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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.14720 |
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| _version_ | 1866929408599654400 |
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| author | Fu, Zunwei Hou, Xianming Wu, Qingyan |
| author_facet | Fu, Zunwei Hou, Xianming Wu, Qingyan |
| contents | In this paper, we introduce the fractional Fourier series on the fractional torus and study some basic facts of fractional Fourier series, such as fractional convolution and fractional approximation. Meanwhile, fractional Fourier inversion and Poisson summation formula are also given. We further discuss the relationship between the decay of fractional Fourier coefficients and the smoothness of a function. Using the properties of fractional Fejer kernel, the pointwise convergence of fractional Fourier series can be established. Finally, we present the applications of fractional Fourier series to fractional partial differential equations with periodic boundary condition. Moreover, we apply approximation methods on the fractional torus to recover the non-stationary signals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_14720 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Convergence of fractional Fourier series on the torus and applications Fu, Zunwei Hou, Xianming Wu, Qingyan Functional Analysis 42A20, 41A35 In this paper, we introduce the fractional Fourier series on the fractional torus and study some basic facts of fractional Fourier series, such as fractional convolution and fractional approximation. Meanwhile, fractional Fourier inversion and Poisson summation formula are also given. We further discuss the relationship between the decay of fractional Fourier coefficients and the smoothness of a function. Using the properties of fractional Fejer kernel, the pointwise convergence of fractional Fourier series can be established. Finally, we present the applications of fractional Fourier series to fractional partial differential equations with periodic boundary condition. Moreover, we apply approximation methods on the fractional torus to recover the non-stationary signals. |
| title | Convergence of fractional Fourier series on the torus and applications |
| topic | Functional Analysis 42A20, 41A35 |
| url | https://arxiv.org/abs/2210.14720 |