The family of Cesàro operators $σ_n^α$, $n \geq 0$ and $α\in [0,1]$, consists of finite rank operators on Banach spaces of analytic functions on the open unit disc. In this work, we investigate these operators as they act on the local Dirichlet spaces $\mathcal{D}_ζ$. It is well-established that they provide a linear a...
E. Dellepiane, J. Mashreghi, Mostafa Nasri et al.· arXiv.org· 0 citations
A sequence of integers $1=a_0<a_1<\cdots<a_k=n$ is called an addition chain of length $k$ if $a_j=a_s+a_t$ with $0\le s,t<j$ for all integers $j\in \{1,2,\ldots,k\}$. We denote by $\ell(n)$ the minimal length of an addition chain leading to $n$. Here we investigate the distribution of the function $\ell$ through the co...
Jean-Marie De Koninck, Nicolas Doyon, W. Verreault· 0 citations
In this paper, we develop a new approach to studying the Fourier transform of Gaussian multiplicative chaos. We determine the Fourier dimension of these random measures on tori for every smooth log-correlated covariance and in every dimension, and prove sharp bounds and exact formulas for chaos on natural classes of bo...
Let $f$ be a Steinhaus or Rademacher random multiplicative function. We use methods from the theory of critical chaos to improve on the best known upper bound for partial sums of random multiplicative functions. In particular, our results imply that for any $\varepsilon>0$, almost surely $$ \Big|\sum_{n\le x}f(n)\Big|...
W. Verreault· 2 citations· ⚡2
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