Fourier characterizations and non-triviality of Gelfand-Shilov spaces, with applications to Toeplitz operators
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866913910509010944 |
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| author | Petersson, Albin |
| author_facet | Petersson, Albin |
| contents | We examine properties of Gelfand-Shilov spaces $S_s$, $S^σ$, $S^σ_s$, $Σ_s$, $Σ^σ$ and $Σ^σ_s$. These are spaces of smooth functions where the functions or their Fourier transforms admit sub-exponential decay. It is determined that $Σ^σ_s$ is nontrivial if and only if $s+ σ > 1$. We find growth estimates on functions and their Fourier transforms in the one-parameter spaces, and we obtain characterizations in terms of estimates of short-time Fourier transforms for these spaces and their duals. Additionally, we determine conditions on the symbols of Toeplitz operators under which the operators are continuous on one-parameter spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_00938 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Fourier characterizations and non-triviality of Gelfand-Shilov spaces, with applications to Toeplitz operators Petersson, Albin Functional Analysis We examine properties of Gelfand-Shilov spaces $S_s$, $S^σ$, $S^σ_s$, $Σ_s$, $Σ^σ$ and $Σ^σ_s$. These are spaces of smooth functions where the functions or their Fourier transforms admit sub-exponential decay. It is determined that $Σ^σ_s$ is nontrivial if and only if $s+ σ > 1$. We find growth estimates on functions and their Fourier transforms in the one-parameter spaces, and we obtain characterizations in terms of estimates of short-time Fourier transforms for these spaces and their duals. Additionally, we determine conditions on the symbols of Toeplitz operators under which the operators are continuous on one-parameter spaces. |
| title | Fourier characterizations and non-triviality of Gelfand-Shilov spaces, with applications to Toeplitz operators |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2202.00938 |