Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectrality of random convolutions generated by finitely many Hadamard
  triples   Let $\{(N_j, B_j, L_j): 1 \le j \le m\}$ be finitely many Hadamard triples in
$\mathbb{R}$. Given a sequence of positive integers $\{n_k\}_{k=1}^\infty$ and
$\omega=(\omega_k)_{k=1}^\infty \in \{1,2,\cdots, m\}^\mathbb{N}$, let
$\mu_{\omega,\{n_k\}}$ be a random infinite convolution given by
$$\mu_{\omega,\{n_k\}} = \delta_{N_{\omega_1}^{-n_1} B_{\omega_1}} *
\delta_{N_{\omega_1}^{-n_1} N_{\omega_2}^{-n_2} B_{\omega_2}} * \cdots *
\delta_{N_{\omega_1}^{-n_1} N_{\omega_2}^{-n_2} \cdots N_{\omega_k}^{-n_k}
B_{\omega_k} }* \cdots. $$ We study the spectrality of $\mu_{\omega,\{ n_k\}}$,
and we show that if the Hadamard triples $\{(N_j, B_j, L_j): 1 \le j \le m\}$
satisfy that $\mathrm{gcd}(B_j - B_j)=1$ for $1 \le j \le m$, then the random
convolution $\mu_{\omega,\{n_k\}}$ is a spectral measure for every $\omega \in
\{1,2,\cdots, m\}^\mathbb{N}$. This implies that we may find a set
$\Lambda_{\omega,\{n_k\}}\subseteq \mathbb{R}$ such that $\big\{ e_\lambda(x) =
e^{-2\pi i \lambda x}: \lambda \in \Lambda_{\omega,\{n_k\}} \big\}$ forms an
orthonormal basis for $L^2(\mu_{\omega,\{ n_k\}})$.

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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg