On the Rationality of the Spectrum
| dc.contributor.author | Madan, Shobha | |
| dc.date.accessioned | 2020-11-20T04:42:02Z | |
| dc.date.available | 2020-11-20T04:42:02Z | |
| dc.date.issued | 2018 | |
| dc.description | Only IISERM authors are available in the record. | |
| dc.description.abstract | Let Ω⊂ℝ be a compact set with measure 1. If there exists a subset Λ⊂ℝ such that the set of exponential functions 𝐸Λ:={𝑒𝜆(𝑥)=𝑒2𝜋𝑖𝜆𝑥|Ω:𝜆∈Λ} is an orthonormal basis for 𝐿2(Ω), then Λ is called a spectrum for the set Ω. A set Ω is said to tile ℝ if there exists a set such that Ω+=ℝ, the set is called a tiling set. A conjecture of Fuglede suggests that spectra and tiling sets are related. Lagarias and Wang (Invent Math 124(1–3):341–365, 1996) proved that tiling sets are always periodic and are rational. That any spectrum is also a periodic set was proved in Bose and Madan (J Funct Anal 260(1):308–325, 2011) and Iosevich and Kolountzakis (Anal PDE 6:819–827, 2013). In this paper, we give some partial results to support the rationality of the spectrum. | en_US |
| dc.identifier.citation | Journal of Fourier Analysis and Applications, 24(4), pp. 1037–1047 | en_US |
| dc.identifier.other | https://doi.org/10.1007/s00041-017-9552-8 | |
| dc.identifier.uri | https://link.springer.com/article/10.1007/s00041-017-9552-8?shared-article-renderer | |
| dc.identifier.uri | http://hdl.handle.net/123456789/1921 | |
| dc.language.iso | en | en_US |
| dc.publisher | Springer Ltd | en_US |
| dc.subject | Spectral sets | en_US |
| dc.subject | Spectrum | en_US |
| dc.subject | Fuglede’s conjecture | en_US |
| dc.subject | Recurrence sequences | en_US |
| dc.subject | Zeros of exponential polynomials | en_US |
| dc.subject | Rationality | en_US |
| dc.title | On the Rationality of the Spectrum | en_US |
| dc.type | Article | en_US |