Sufficient conditions for the spectrality of self-affine measures with prime determinant

• Autorzy: Jian-Lin Li
• Języki publikacji: EN

Abstrakty

EN

Let $μ_{M,D}$ be a self-affine measure associated with an expanding matrix M and a finite digit set D. We study the spectrality of $μ_{M,D}$ when |det(M)| = |D| = p is a prime. We obtain several new sufficient conditions on M and D for $μ_{M,D}$ to be a spectral measure with lattice spectrum. As an application, we present some properties of the digit sets of integral self-affine tiles, which are connected with a conjecture of Lagarias and Wang.

Kategorie tematyczne

• 42C05: Orthogonal functions and polynomials, general theory
• 28A80: Fractals
• 46C05: Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 220
• Numer: 1
• Strony: 73-86

Daty

wydano

2014

Twórcy

autor

Jian-Lin Li

• College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, P.R. China

Identyfikatory

DOI

10.4064/sm220-1-4