Spectral properties of unions of intervals and groups of local translations
Abstract
In connection to the Fuglede conjecture, and to Fuglede's original work Fug74, we study one-parameter unitary groups associated to self-adjoint extensions of the differential operator Df=12πif' 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 which admit orthogonal bases of exponential functions (also called spectral sets).
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