相关论文: $L^p$ properties for Gaussian random series
In this paper we explore the influence of the shape parameter in the gaussian function on error estimates and present a set of criteria for its optimal choice.
We study $H^p$ spaces of Dirichlet series, called $\mathcal{H}^p$, for the range $0<p< \infty$. We begin by showing that two natural ways to define $\mathcal{H}^p$ coincide. We then proceed to study some linear space properties of…
We consider a measurable stationary Gaussian stochastic process. A criterion for testing hypotheses about the covariance function of such a process using estimates for its norm in the space $L_p(\mathbb {T}),\,p\geq1$, is constructed.
Two types of Gaussian processes, namely the Gaussian field with generalized Cauchy covariance (GFGCC) and the Gaussian sheet with generalized Cauchy covariance (GSGCC) are considered. Some of the basic properties and the asymptotic…
We study the regularity properties of Gaussian fields defined over spheres cross time. In particular, we consider two alternative spectral decompositions for a Gaussian field on $\mathbb{S}^d \times \mathbb{R}$. For each decomposition, we…
This manuscript reviews theoretical results and applications related to quadratic forms in Gaussian random variables. It summarizes definitions, canonical representations, exact and approximate distributional results, numerical inversion…
We investigate $L^p$ regularity of weighted Bergman projections on the unit disc and $L^p$ regularity of ordinary Bergman projections in higher dimensions.
Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…
We establish local $(L^p,L^q)$ mapping properties for averages on curves. The exponents are sharp except for endpoints.
The paper study the discrete sets of translations of the Gaussian function that span the spaces L1(R) and L2(R).
$L^p$ spaces are investigated for vector lattice-valued functions, with respect to filter convergence. As applications, some classical inequalities are extended to the vector lattice context, and some properties of the Brownian Motion and…
Locally weighted regression was created as a nonparametric learning method that is computationally efficient, can learn from very large amounts of data and add data incrementally. An interesting feature of locally weighted regression is…
The study of the global mapping properties of arbitrary Dirichlet L-functions is undertaken. The results are applied to the proof of the Generalized Riemann Hypothesis.
We have derived some new results for the Mellin transform formulas, as well as for the Gauss hypergeometric function. Also, we have found the connection between the Legendre functions of the second kind. Some of the results obtained we used…
Variational Gaussian process (GP) approximations have become a standard tool in fast GP inference. This technique requires a user to select variational features to increase efficiency. So far the common choices in the literature are…
We introduce a new Gaussian process, a generalization of both fractional and subfractional Brownian motions, which could serve as a good model for a larger class of natural phenomena. We study its main stochastic properties and some…
We study the hole probability of Gaussian entire functions. More specifically, we work with entire functions in Taylor series form with i.i.d complex Gaussian random variables and arbitrary non-random coefficients. A hole is the event where…
We study the regularity properties of random wavelet series constructed by multiplying the coefficients of a deterministic wavelet series with unbounded I.I.D. random variables. In particular, we show that, at the opposite to what happens…
We consider Gaussian Besov spaces obtained by real interpolation and Riemann-Liouville operators of fractional integration on the Gaussian space and relate the fractional smoothness of a functional to the regularity of its heat extension.…
We investigate geometric properties of a class of trace functions expressed in terms of the deformed logarithmic and exponential functions. These trace functions and their properties may be of independent interest. We use them in particular…