Kolountzakis, Mihail N. and Lev, Nir and Matolcsi, Máté (2025) Maximality and completeness of orthogonal exponentials on the cube. EXPOSITIONES MATHEMATICAE. No. 125682. ISSN 0723-0869 (In Press)
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Abstract
It is possible to have a packing by translates of a cube that is maximal (i.e. no other cube can be added without overlapping) but does not form a tiling. In the long running analogy of packing and tiling to orthogonality and completeness of exponentials on a domain, we pursue the question whether one can have maximal orthogonal sets of exponentials for a cube without them being complete. We prove that this is not possible in dimensions 1 and 2, but is possible in dimensions 3 and higher. We provide several examples of such maximal incomplete sets of exponentials, differing in size, and we raise relevant questions. We also show that even in dimension 1 there are sets which are spectral (i.e. have a complete set of orthogonal exponentials) and yet they also possess maximal incomplete sets of orthogonal exponentials. © 2025 The Author(s)
| Item Type: | Article |
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| Additional Information: | University of Crete, Department of Applied Mathematics, Rethymnon, Greece Institute of Computer Science, Heraklion, Greece Bar-Ilan University, Ramat Gan, Israel Alfréd Rényi Institute of Mathematics, Budapest, Hungary Budapest University of Technology and Economics, Department of Analysis and Operations Research, Budapest, Hungary Export Date: 01 September 2025; Cited By: 0 |
| Uncontrolled Keywords: | PACKING; Tiling; Spectral set; orthogonal exponentials; |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 02 Sep 2025 08:23 |
| Last Modified: | 02 Sep 2025 08:23 |
| URI: | https://real.mtak.hu/id/eprint/223115 |
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