相关论文: Riesz Means and Beurling Moving Averages
We summarize some of the recent developments which link certain problems in combinatorial theory related to random growth to random matrix theory.
In the interpretation of experimental data, one is actually looking for plausible explanations. We look for a measure of plausibility, with which we can compare different possible explanations, and which can be combined when there are…
We introduce a natural definition of Riesz measures and Wishart laws associated to an $\Omega$-positive (virtual) quadratic map, where $\Omega \subset \real^n$ is a regular open convex cone. We give a general formula for moments of the…
We consider the Grushin operator with drift which is symmetric with respect to a measure having exponential growth. For the corresponding Riesz transforms, we study strong-type $(p, p)$, $1 < p < \infty$, and weak-type $(1, 1)$ boundedness.
In this paper, we investigate the $L^{p}$-boundedness of the Riesz means and the $L^{p_{1}}\times L^{p_{2}}\rightarrow L^{p}$ boundedness of the bilinear Riesz means on M\'{e}tivier groups. M\'{e}tivier groups are generalization of…
An estimate of Beurling states that if K is a curve from 0 to the unit circle in the complex plane, then the probability that a Brownian motion starting at -eps reaches the unit circle without hitting the curve is bounded above by c…
Beurling density plays a key role in the study of frame-spectrality of normalized Lebesgue measure restricted to a set. Accordingly, in this paper, the authors study the $s$-Beurling densities of regular maximal orthogonal sets of a class…
Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…
We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…
Properties of weighted averages are studied for the general case that the individual measurements are subject to hidden correlations and have asymmetric statistical as well as systematic errors. Explicit expressions are derived for an…
A variety of interesting parameters may depend on high dimensional regressions. Machine learning can be used to estimate such parameters. However estimators based on machine learners can be severely biased by regularization and/or model…
This paper addresses the problem of regularity properties of functions represented as an expansion in a wavelet basis with random coefficients in terms of finiteness of their Besov norm with probability 1. Such representations are used to…
We introduce a moving average summability method, which is proved to be equivalent with the logarithmic $\ell$-method. Several equivalence and Tauberian theorems are given. A strong law of large numbers is also proved.
We note that the necessary and sufficient conditions established by Marcel Riesz for the inclusion of regular N\"orlund summation methods are in fact applicable quite generally.
Riesz Theorem establishes a correspondence between the set of $\sigma$-additive regular Borel measures and the set of linear positively defined functionals. We consider an idempotent analogue of this correspondence between possibility…
Beurling slow variation is generalized to Beurling regular variation. A Uniform Convergence Theorem, not previously known, is proved for those functions of this class that are measurable or have the Baire property. This permits their…
We give an improvement of sharp Berezin type bounds on the Riesz means $\sum_k(\Lambda-\lambda_k)_+^\sigma$ of the eigenvalues $\lambda_k$ of the Dirichlet Laplacian in a domain if $\sigma\geq 3/2$. It contains a correction term of the…
An inequality of Brascamp-Lieb-Luttinger generalizes the Riesz-Sobolev inequality, stating that certain multilinear functionals, acting on nonnegative functions of one real variable with prescribed distribution functions, are maximized when…
This paper studies posterior concentration behavior of the base probability measure of a Dirichlet measure, given observations associated with the sampled Dirichlet processes, as the number of observations tends to infinity. The base…
If $x_1,\dots,x_m$ are finitely many points in $\mathbb{R}^d$, let $E_\epsilon=\cup_{i=1}^m\,x_i+Q_\epsilon$, where $Q_\epsilon=\{x\in \mathbb{R}^d,\,\,|x_i|\le \epsilon/2, \, i=1,...,d\}$ and let $\hat f$ denote the Fourier transform of…