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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.18625 |
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| _version_ | 1866911019091099648 |
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| author | Ducasse, Bryan Dutkay, Dorin Ervin Fernandez, Colby |
| author_facet | Ducasse, Bryan Dutkay, Dorin Ervin Fernandez, Colby |
| contents | In connection to the Fuglede conjecture, and to Fuglede's original work \cite{Fug74}, we study one-parameter unitary groups associated to self-adjoint extensions of the differential operator $Df=\frac1{2πi}f'$ on a union of finite intervals. We present a formula for such unitary groups and we use it to discover some geometric properties of such sets in $\br$ which admit orthogonal bases of exponential functions (also called spectral sets). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18625 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral properties of unions of intervals and groups of local translations Ducasse, Bryan Dutkay, Dorin Ervin Fernandez, Colby Functional Analysis Spectral Theory 47E05, 42A16 In connection to the Fuglede conjecture, and to Fuglede's original work \cite{Fug74}, we study one-parameter unitary groups associated to self-adjoint extensions of the differential operator $Df=\frac1{2πi}f'$ on a union of finite intervals. We present a formula for such unitary groups and we use it to discover some geometric properties of such sets in $\br$ which admit orthogonal bases of exponential functions (also called spectral sets). |
| title | Spectral properties of unions of intervals and groups of local translations |
| topic | Functional Analysis Spectral Theory 47E05, 42A16 |
| url | https://arxiv.org/abs/2506.18625 |