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Mathematical problem From Wikipedia, the free encyclopedia
Fuglede's conjecture is an open problem in mathematics proposed by Bent Fuglede in 1974. It states that every domain of (i.e. subset of with positive finite Lebesgue measure) is a spectral set if and only if it tiles by translation.[1]
Spectral sets in
A set with positive finite Lebesgue measure is said to be a spectral set if there exists a such that is an orthogonal basis of . The set is then said to be a spectrum of and is called a spectral pair.
Translational tiles of
A set is said to tile by translation (i.e. is a translational tile) if there exist a discrete set such that and the Lebesgue measure of is zero for all in .[2]
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