Let $ R $ be an expanding matrix with integer entries, and let $ B, L $ be finite integer digit
sets so that $(R, B, L) $ form a Hadamard triple on ${\mathbb {R}}^ d $ in the sense that the …

Abstract Let {D k} k= 1∞ be a sequence of digit sets in N and let {bk} k= 1∞ be a sequence
of integer numbers bigger than 1. We call the family {fk, D k (x)= bk− 1 (x+ d): d∈ D k, k⩾ 1} a …

We introduce a duality for affine iterated function systems (AIFS) which is naturally motivated
by group duality in the context of traditional harmonic analysis. Our affine systems yield …

Abstract Let {A k} k= 1∞ be a sequence of finite subsets of R d satisfying that# A k≥ 2 for all
integers k≥ 1. In this paper, we first give a sufficient and necessary condition for the …

For a finite set D⊂ Z and an integer b≥ 2, we say that (b, D) is compatible with C⊂ Z if [e− 2
π idc/b] d∈ D, c∈ C is a Hadamard matrix. Let δ E= 1# E∑ a∈ E δ a denote the uniformly …

Spectral sets and tiles in Zp2×Zq2 - ScienceDirect Skip to main contentSkip to article Elsevier
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It is well known that if a finite set A⊂ Z tiles the integers by translations, then the translation
set must be periodic, so that the tiling is equivalent to a factorization A⊕ B= ZM of a finite …

Combinatorial and harmonic-analytic methods for integer tilings Page 1 Forum of Mathematics,
Pi (2022), Vol. 10:e8 1–46 doi:10.1017/fmp.2022.3 RESEARCH ARTICLE Combinatorial and …

Fuglede’s conjecture holds in $$\mathbb {Q}_{p}$$ | SpringerLink Skip to main content
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Fuglede's conjecture states that for a subset of a locally compact abelian group with positive
and finite Haar measure, there exists a subset of the dual group of which is an orthogonal …