On Fuglede's conjecture for three intervals
Classical Analysis and ODEs
2010-02-23 v2
Abstract
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.
Keywords
Cite
@article{arxiv.0803.0049,
title = {On Fuglede's conjecture for three intervals},
author = {Debashish Bose and C. P. Anil Kumar and R. Krishnan and Shobha Madan},
journal= {arXiv preprint arXiv:0803.0049},
year = {2010}
}
Comments
21 pages