Gohberg-Krupnik Localisation for Discrete Wiener-Hopf Operators on Orlicz Sequence Spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914036309819392 |
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| author | Karlovych, Oleksiy Thampi, Sandra Mary |
| author_facet | Karlovych, Oleksiy Thampi, Sandra Mary |
| contents | Let $Φ$ be an $N$-function whose Matuszewska-Orlicz indices satisfy $1<α_Φ\leβ_Φ<\infty$. Using these indices, we introduce ``interpolation friendly" classes of Fourier multipliers $M_{[Φ]}$ and $M_{\langleΦ\rangle}$ such that $M_{[Φ]}\subset M_{\langleΦ\rangle}\subset M_Φ$, where $M_Φ$ is the Banach algebra of all Fourier multipliers on the reflexive Orlicz sequence space $\ell^Φ(\mathbb{Z})$. Applying the Gohberg-Krupnik localisation in the corresponding Calkin algebra, the study of Fredholmness of the discrete Wiener-Hopf operator $T(a)$ with $a\in M_{\langleΦ\rangle}$ is reduced to that of $T(a_τ)$ for certain, potentially easier to study, local representatives $a_τ\in M_{[Φ]}$ of $a$ at all points $τ\in[-π,π)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11203 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gohberg-Krupnik Localisation for Discrete Wiener-Hopf Operators on Orlicz Sequence Spaces Karlovych, Oleksiy Thampi, Sandra Mary Functional Analysis Let $Φ$ be an $N$-function whose Matuszewska-Orlicz indices satisfy $1<α_Φ\leβ_Φ<\infty$. Using these indices, we introduce ``interpolation friendly" classes of Fourier multipliers $M_{[Φ]}$ and $M_{\langleΦ\rangle}$ such that $M_{[Φ]}\subset M_{\langleΦ\rangle}\subset M_Φ$, where $M_Φ$ is the Banach algebra of all Fourier multipliers on the reflexive Orlicz sequence space $\ell^Φ(\mathbb{Z})$. Applying the Gohberg-Krupnik localisation in the corresponding Calkin algebra, the study of Fredholmness of the discrete Wiener-Hopf operator $T(a)$ with $a\in M_{\langleΦ\rangle}$ is reduced to that of $T(a_τ)$ for certain, potentially easier to study, local representatives $a_τ\in M_{[Φ]}$ of $a$ at all points $τ\in[-π,π)$. |
| title | Gohberg-Krupnik Localisation for Discrete Wiener-Hopf Operators on Orlicz Sequence Spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2509.11203 |