In this paper 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. For the general case we change our
approach to get information on the structure of the spectrum for the n-interval
case. Finally, we use symbolic computations on Mathematica, and prove this part
of the conjecture with an additional assumption on the spectrum.Comment: 21 page