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1,159 results on '"Li, Jinjun"'

4. Spectra of the Sierpi\'{n}ski type spectral measure and their Beurling dimensions

Author

Li, Jinjun and Wu, Zhiyi

Subjects
Mathematics - Number Theory
Abstract

In this paper, we study the structure of the spectra for the Sierpi\'{n}ski type spectral measure $\mu_{A,\mathcal{D}}$ on $\mathbb{R}^2$. We give a sufficient and necessary condition for the family of exponential functions $\{e^{-2\pi i\langle\lambda, x\rangle}: \lambda\in\Lambda\}$ to be a maximal orthogonal set in $L^2(\mu_{A,\mathcal{D}})$. Based on this result, we obtain a class of regular spectra of $\mu_{A,\mathcal{D}}$. Moreover, we discuss the Beurling dimensions of the spectra and obtain the optimal upper bound of Beurling dimensions of all spectra, which is in stark contrast with the case of self-similar spectral measure. An intermediate property about the Beurling dimension of the spectra is obtained.

Published
2023

5. On the intermediate value property of spectra for a class of Moran spectral measures

Author

Li, Jinjun and Wu, Zhiyi

Subjects
Mathematics - Number Theory, Mathematics - Classical Analysis and ODEs
Abstract

We prove that the Beurling dimensions of the spectra for a class of Moran spectral measures are between $0$ and their upper entropy dimensions. Moreover, for such a Moran spectral measure $\mu$, we show that the Beurling dimension for the spectra of $\mu$ has the intermediate value property: let $t$ be any value between $0$ and the upper entropy dimension of $\mu$, then there exists a spectrum whose Beurling dimension is $t.$ In particular, this result settles affirmatively a conjecture involving spectral Bernoulli convolution proposed by Fu, He and Wen in [J. Math. Pures Appl. 116 (2018), 105--131]. Furthermore, we prove that the set of the spectra whose Beurling dimensions are equal to any fixed value between $0$ and $\ue \mu$ has the cardinality of the continuum.

Published
2023

49. On Assouad dimension and arithmetic progressions in sets defined by digit restrictions

Author

Li, Jinjun, Wu, Min, and Xiong, Ying

Subjects
Mathematics - Classical Analysis and ODEs, 28A80, 42A38
Abstract

We show that the set defined by digit restrictions contains arbitrarily long arithmetic progressions if and only if its Assouad dimension is one. Moreover, we show that for any $0\le s\le 1$, there exists some set on $\mathbb{R}$ with Hausdorff dimension $s$ whose Fourier dimension is zero and it contains arbitrarily long arithmetic progressions., Comment: 12 pages, 1 figures. We consider more general model and gave a new proof for Proposition 3.1

Published
2017

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