The Fuglede conjecture holds in ℤp× ℤp
| Autor: | Jonathan Pakianathan, Azita Mayeli, Alex Iosevich |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Numerical Analysis
Conjecture Applied Mathematics 010102 general mathematics Galois theory 020206 networking & telecommunications Context (language use) 02 engineering and technology Function (mathematics) Translation (geometry) 01 natural sciences Combinatorics symbols.namesake Finite field Fourier transform 0202 electrical engineering electronic engineering information engineering symbols 0101 mathematics Linear combination Analysis Mathematics |
| Zdroj: | Analysis & PDE. 10:757-764 |
| ISSN: | 1948-206X 2157-5045 |
| DOI: | 10.2140/apde.2017.10.757 |
| Popis: | In this paper we study subsets E of ℤpd such that any function f : E → ℂ can be written as a linear combination of characters orthogonal with respect to E. We shall refer to such sets as spectral. In this context, we prove the Fuglede conjecture in ℤp2, which says in this context that E ⊂ ℤp2 is spectral if and only if E tiles ℤp2 by translation. Arithmetic properties of the finite field Fourier transform, elementary Galois theory and combinatorial geometric properties of direction sets play the key role in the proof. The proof relies to a significant extent on the analysis of direction sets of Iosevich et al. (Integers 11 (2011), art. id. A39) and the tiling results of Haessig et al. (2011). |
| Databáze: | OpenAIRE |
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