Maximal Noncompactness of Wiener-Hopf Operators
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909930149117952 |
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| author | Karlovych, Oleksiy Shargorodsky, Eugene |
| author_facet | Karlovych, Oleksiy Shargorodsky, Eugene |
| contents | Let $X(\mathbb{R})$ be a separable translation-invariant Banach function space and $a$ be a Fourier multiplier on $X(\mathbb{R})$. We prove that the Wiener-Hopf operator $W(a)$ with symbol $a$ is maximally noncompact on the space $X(\mathbb{R}_+)$, that is, its Hausdorff measure of noncompactness, its essential norm and its norm are all equal. This equality for the Hausdorff measure of noncompactness of $W(a)$ is new even in the case of $X(\mathbb{R})=L^p(\mathbb{R})$ with $1\le p<\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximal Noncompactness of Wiener-Hopf Operators Karlovych, Oleksiy Shargorodsky, Eugene Functional Analysis Let $X(\mathbb{R})$ be a separable translation-invariant Banach function space and $a$ be a Fourier multiplier on $X(\mathbb{R})$. We prove that the Wiener-Hopf operator $W(a)$ with symbol $a$ is maximally noncompact on the space $X(\mathbb{R}_+)$, that is, its Hausdorff measure of noncompactness, its essential norm and its norm are all equal. This equality for the Hausdorff measure of noncompactness of $W(a)$ is new even in the case of $X(\mathbb{R})=L^p(\mathbb{R})$ with $1\le p<\infty$. |
| title | Maximal Noncompactness of Wiener-Hopf Operators |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2509.17451 |