The Fuglede spectral conjecture holds for convex planar domains

By Alex Iosevich, Nets Hawk Katz, Terence Tao. 2003

128 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/cfb449a4a5f765cf12cf64e7fce1c74ba20992d8

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Combining Riesz bases (2012, background): “k=1 ‖fk‖ (2), (3) where c2 is a positive constant, not depending on f .”
The Fuglede conjecture for convex domains is true in all dimensions (2019, background): “so be centrally symmetric. The proof is based on a development of the argument in [KP02]. The last condition (iv) was addressed so far only in dimensions d = 2 and 3. Iosevich, Katz and Tao proved in [IKT03] that if a convex polygon Ω ⊂ R2 is a spectral set, then it must be either a parallelogram or”
Fuglede's spectral set conjecture for convex polytopes (2016, unknown): “This result is essentially contained in [Iosevich et al. 2003], although it was not stated explicitly in that paper.”
Multi-tiling and Riesz bases (2012, background): “convex polygon has a spectrum only if it is (up to an affine transformation) either a square or a hexagon [6].”
Fuglede's conjecture on cyclic groups of order pnq (2016, background): “ure when the spectrum or the tiling complement of Ω is a lattice. Later on, the conjecture was proved for various families of subsets by numerous authors, for example, for 2-dimensional convex bodies [7], unions of two intervals in R[11], etc. Against the current of research on this subject, Tao dis”
Weak convergence and spectrality of infinite convolutions (2022, background): “Although the both directions of Fuglede’s conjecture were disproved by Tao [52] and the others [22, 23, 32, 33, 43] for d ≥ 3, the connection between spectrality and tiling has generated a lot of interest, and some affirmative results have been proved for special cases [29,34].”