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\iteman{io-port 06037179}
\itemau{Bose, Debashish; Kumar, C.P.Anil; Krishnan, R.; Madan, Shobha}
\itemti{On Fuglede's conjecture for three intervals.}
\itemso{Online J. Anal. Comb. 5, Article 1, 24 p., electronic only (2010).}
\itemab
Summary: We prove the ``tiling implies spectral" part of Fuglede's paper for the case of three intervals. Then we prove the ``spectral implies tiling" part of the conjecture for the case of three equal intervals as also when the intervals have lengths $1/2$, $1/4$, $1/4$. Next, we consider a set $\Omega\subset\mathbb{R}$ which is a union of $n$ intervals. If $\Omega$ is a spectral set, we prove a structure theorem for the spectrum provided the spectrum is assumed to be contained in some lattice. The method of this proof has some implications on the spectral implies tiling part of Fuglede's conjecture for three intervals. In the final step in the proof, we need a symbolic computation using Mathematica. Finally with one additional assumption we can conclude that the spectral implies tiling holds in this case.
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\itemut{Fuglede's conjecture; three intervals; tiling implies spectral; spectral implies tiling; symbolic computation}
\itemli{}
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