# Structure of the spectrum and Fuglede's Conjecture for three intervals

Department of Mathematics, I.I.T. Kanpur
INDIA

given at  strobl07 (21.06.07 09:00)
id:  566
length:  25min
status:  accepted
type:  talk
ABSTRACT:
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\title[Fuglede's Conjecture]{Structure of spectrum and Fuglede's conjecture for three intervals}
\author{Debashish Bose}

\address{Department of Mathematics, Indian Institute of Technology, Kanpur 208016, India}
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\begin{abstract}
We first prove that if $\Omega \subset \rr$ is a union of $n$ intervals and is a spectral set, with a spectrum contained in a lattice, then the spectrum is rational. The method of this proof has some implications on the {\it spectral implies tiling} part of Fuglede's conjecture for three intervals, which we prove under the hypothesis that the spectrum is contained in a lattice. At one step in the proof, we need a symbolic computation using {\it Mathematica} to reduce to the equal interval case. This latter case is then taken care of explicitly. Finally we also prove the converse part, {\it tiling implies spectral} for the three interval case.

\end{abstract}

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