相关论文: $L^p$ properties for Gaussian random series

Using the spectral resolution of the multiplication operator on the Schwartz class of $L^2(\mathbb{R},\mathbb{C})$, we compute the characteristic function of the cube of a Gaussian random variable.

We study integrability and continuity properties of random series of Hermite functions. We get optimal results which are analogues to classical results concerning Fourier series, like the Paley-Zygmund or the Salem-Zygmund theorems. We also…

We consider a set of one-dimensional transformations of Gaussian random functions. Under natural assumptions we obtain a connection between $L_2$-small ball asymptotics of the transformed function and of the original one. Also the explicit…

We consider Gaussian subordinated L\'evy fields (GSLFs) that arise by subordinating L\'evy processes with positive transformations of Gaussian random fields on some spatial domain $\mathcal{D}\subset \mathbb{R}^d$, $d\geq 1$. The resulting…

The authors survey recent results in special functions, particularly the gamma function and the Gaussian hypergeometric function.

In this paper we study the regularity properties of the Gaussian Bessel potentials and Gaussian Bessel fractional derivatives on variable Gaussian Besov-Lipschitz spaces $B_{p(\cdot),q(\cdot)}^{\alpha}(\gamma_{d}),$ that were defined in a…

In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture…

In this paper, we will discuss several radii problems related to Wright Function involving four parameters.

We begin with isotropic Gaussian random fields, and show how the Bochner-Godement theorem gives a natural way to describe their covariance structure. We continue with a study of Mat\'ern processes on Euclidean space, spheres, manifolds and…

Gaussian particles provide a flexible framework for modelling and simulating three-dimensional star-shaped random sets. In our framework, the radial function of the particle arises from a kernel smoothing, and is associated with an…

We generalize a Theorem of Ricci and count Gaussian primes $\mathfrak{p}$ with short interval restrictions on both the norm and the argument of $\mathfrak{p}$.

We first give some apriori estimates of positive radial solutions of $p$-Laplace H\'enon equation. Then we study the local and global properties of those solutions. Finally, we generalize some radial results to the nonradial case.

A transference result of the L^p continuity of the Jacobi Littlewood-Paley g-function to the Gaussian and Laguerre Littlewood-Paley g-function.

We study the hole probability of Gaussian random entire functions. More specifically, we work with entire functions in Taylor series form with i.i.d complex Gaussian coefficients. A hole is the event where the function has no zeros in a…

We study sampling properties of the zero set of the Gaussian entire function on Fock spaces. Firstly, we relax Seip and Wallst\'en's density and separation conditions for sampling sets on Fock spaces to obtain weighted inequalities for sets…

In this paper, we study some properties of multivariate gamma function and zonal polynomials.

We study Spatial Logistic Gaussian Process (SLGP) models for non-parametric estimation of probability density fields using scattered samples of heterogeneous sizes. SLGPs are examined from the perspective of random measures and their…

We investigate the complex Gaussian as well as non-Gaussian distributed random analytical and entire functions (complex entire random field) and calculate their domain of definiteness (radius of convergence) as well as some important…

Let $\Gamma$ be a graph equipped with a Markov operator $P$. We introduce discrete fractional Littlewood-Paley square functionals and prove their $L^p$-boundedness under various geometric assumptions on $\Gamma$.

We study Lusin-measurable functions with values in locally convex spaces. In particular, the behavior of pointwise limits of sequences of Lusin-measurable functions and exhibit pathological phenomena arising in the nonmetrizable setting.…