Abstract
Spectra and tilings play an important role in analysis and geometry respectively. The relations between spectra and tilings have baffled the mathematicians for a long time. Many conjectures, such as the Fuglede conjecture, are placed on the establishment of relations between spectra and tilings, although there are no desired results. In the present paper we derive some characteristic properties of spectra and tilings which highlight certain duality properties between them.
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