On spectral Cantor-Moran measures and a variant of Bourgain's sum of sine problem

An, Li-Xiang; Fu, Xiaoye; Lai, Chun–Kit

doi:10.1016/j.aim.2019.04.014

Cited by 74 publications

(47 citation statements)

References 34 publications

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“…Since the vector v k is nonzero, by (8•38), we obtain that the rank of the matrix M k has to be smaller than Ω k . Therefore we conclude that the the rank of the matrix M k is Ω k − 1 and consequently that Ω k = D k , which implies (2). Moreover, we have M k = H k .…”

Section: Proof Of Main Theoremmentioning

confidence: 70%

On $p$-adic spectral measures

Shi

2020

Preprint

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Section: Proof Of Main Theoremmentioning

confidence: 70%

On $p$-adic spectral measures

Shi

2020

Preprint

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“…Many affirmative results have been obtained in [1][2][3][4][5]11,15,19,27,32]. When all Hadamard triples are the same one, the infinite convolution reduces to a self-affine measure (which is called a self-similar measure for d = 1).…”

Section: Question Given a Sequence Of Hadamard Triplesmentioning

confidence: 97%

Spectrality of random convolutions generated by finitely many Hadamard triples

Li¹,

Miao²,

Wang³

2022

Preprint

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“…Now we will provec 2 A * Z( μ M, D) ⊂ Z( μM,D ), where c 2 = N (p−1)(p n −1) . Note first that B * A * = I (mod p) and Z(m D) ⊂ En p + Z n .…”

mentioning

confidence: 89%

The spectrality of self-affine measure under the similarity transformation of $GL_n(p)$

Liu,

Wang

2020

Preprint

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Let µ M,D be the self-affine measure generated by an expanding integer matrix M ∈ M n (Z) and a finite digit set D ⊂ Z n . It is well known that the two measures µ M,D and µ M, D have the same spectrality if M = B −1 MB and D = B −1 D, where B ∈ M n (R) is a nonsingular matrix. This fact is usually used to simplify the digit set D or the expanding matrix M. However, it often transforms integer digit set D or expanding matrix M into real, which brings many difficulties to study the spectrality of µ M, D. In this paper, we introduce a similarity transformation of general linear group GL n (p) for some self-affine measures, and discuss their spectrality. This kind of similarity transformation can keep the integer properties of D and M simultaneously, which leads to many advantages in discussing the spectrality of self-affine measures. As an application, we extend some well-known spectral self-affine measures to more general forms.

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On spectral Cantor-Moran measures and a variant of Bourgain's sum of sine problem

Cited by 74 publications

References 34 publications

On $p$-adic spectral measures

On $p$-adic spectral measures

Spectrality of random convolutions generated by finitely many Hadamard triples

The spectrality of self-affine measure under the similarity transformation of $GL_n(p)$

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