“Spectral implies Tiling” for three intervals revisited
Bose, Anil Kumar, Krishnan and Madan (2010) showed that “Tiling implies Spectral” holds for a union of three intervals and the reverse implication was studied under certain restrictive hypotheses on the associated spectrum. In this paper, we reinvestigate the “Spectral implies Tiling” part of Fugled...
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| Published in | Forum mathematicum Vol. 26; no. 4; pp. 1247 - 1260 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin
De Gruyter
01.07.2014
Walter de Gruyter GmbH |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0933-7741 1435-5337 |
| DOI | 10.1515/forum-2011-0129 |
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| Abstract | Bose, Anil Kumar, Krishnan and Madan (2010)
showed that “Tiling implies Spectral” holds
for a union of three intervals and the reverse implication was
studied under certain restrictive hypotheses on the associated
spectrum. In this paper, we reinvestigate the “Spectral implies
Tiling” part of Fuglede's conjecture for the three interval case.
We first show that the “Spectral implies Tiling” for two intervals
follows from the simple fact that two distinct circles have at most
two points of intersections. We then attempt this for the case of
three intervals and except for one situation are able to prove
“Spectral implies Tiling”. Finally, for the exceptional case, we
show a connection to a problem of generalized Vandermonde
varieties. |
|---|---|
| AbstractList | Bose, Anil Kumar, Krishnan and Madan (2010)
showed that “Tiling implies Spectral” holds
for a union of three intervals and the reverse implication was
studied under certain restrictive hypotheses on the associated
spectrum. In this paper, we reinvestigate the “Spectral implies
Tiling” part of Fuglede's conjecture for the three interval case.
We first show that the “Spectral implies Tiling” for two intervals
follows from the simple fact that two distinct circles have at most
two points of intersections. We then attempt this for the case of
three intervals and except for one situation are able to prove
“Spectral implies Tiling”. Finally, for the exceptional case, we
show a connection to a problem of generalized Vandermonde
varieties. Bose, Anil Kumar, Krishnan and Madan (2010) showed that "Tiling implies Spectral" holds for a union of three intervals and the reverse implication was studied under certain restrictive hypotheses on the associated spectrum. In this paper, we reinvestigate the "Spectral implies Tiling" part of Fuglede's conjecture for the three interval case. We first show that the "Spectral implies Tiling" for two intervals follows from the simple fact that two distinct circles have at most two points of intersections. We then attempt this for the case of three intervals and except for one situation are able to prove "Spectral implies Tiling". Finally, for the exceptional case, we show a connection to a problem of generalized Vandermonde varieties. [PUBLICATION ABSTRACT] |
| Author | Madan, Shobha Bose, Debashish |
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| Snippet | Bose, Anil Kumar, Krishnan and Madan (2010)
showed that “Tiling implies Spectral” holds
for a union of three intervals and the reverse implication was
studied... Bose, Anil Kumar, Krishnan and Madan (2010) showed that "Tiling implies Spectral" holds for a union of three intervals and the reverse implication was studied... |
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| SubjectTerms | 42A99 Fuglede's conjecture Spectral sets spectrum tiling |
| Title | “Spectral implies Tiling” for three intervals revisited |
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