Compactness for pseudo-differential and Toeplitz operators on modulation spaces
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914467553476608 |
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| author | Nabizadeh-Morsalfard, Elmira Pfeuffer, Christine Teofanov, Nenad Toft, Joachim |
| author_facet | Nabizadeh-Morsalfard, Elmira Pfeuffer, Christine Teofanov, Nenad Toft, Joachim |
| contents | We deduce various norm equivalences, and convolution estimates for the modulation space $M^{\sharp ,q}_{(ω)}$ consisting of all $f\in M^{\infty ,q}_{(ω)}$ such that $|V_ϕf \cdot ω|$ satisfies a mild vanishing condition at infinity. We prove that $M^{\sharp ,q}_{(ω)}$ is the completion of the Gelfand-Shilov space $Σ_1$ under the $M^{\infty ,q}_{(ω)}$ norm. We use these results to deduce compactness for $Ψ$DO $\op (\mathfrak a )$, with $\mathfrak a \in M^{\sharp ,q}_{(ω)}$, $0<q\le 1$, when acting on a broad family of modulation spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10921 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Compactness for pseudo-differential and Toeplitz operators on modulation spaces Nabizadeh-Morsalfard, Elmira Pfeuffer, Christine Teofanov, Nenad Toft, Joachim Functional Analysis We deduce various norm equivalences, and convolution estimates for the modulation space $M^{\sharp ,q}_{(ω)}$ consisting of all $f\in M^{\infty ,q}_{(ω)}$ such that $|V_ϕf \cdot ω|$ satisfies a mild vanishing condition at infinity. We prove that $M^{\sharp ,q}_{(ω)}$ is the completion of the Gelfand-Shilov space $Σ_1$ under the $M^{\infty ,q}_{(ω)}$ norm. We use these results to deduce compactness for $Ψ$DO $\op (\mathfrak a )$, with $\mathfrak a \in M^{\sharp ,q}_{(ω)}$, $0<q\le 1$, when acting on a broad family of modulation spaces. |
| title | Compactness for pseudo-differential and Toeplitz operators on modulation spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2604.10921 |