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arXiv · 2506.18625

Spectral properties of unions of intervals and groups of local translations

Bryan Ducasse·Dorin Ervin Dutkay·Colby Fernandez
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Abstract

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).

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Bryan Ducasse, Dorin Ervin Dutkay, Colby Fernandez. 2026-06-24. Spectral properties of unions of intervals and groups of local translations. https://arxiv.org/abs/2506.18625

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