Related papers: On the Spectral Large Sieve Inequality for $\mathr…
This paper deals with spectral inequalities for one-dimensional Schr\"odinger operators with potentials bounded between two increasing functions (weights). The spectral inequality allows one to estimate the norm of a function with bounded…
An inverse problem in spectroscopy is considered. The objective is to restore the discrete spectrum from observed spectrum data, taking into account the spectrometer's line spread function. The problem is reduced to solution of a system of…
Bayesian synthetic likelihood (BSL) is a popular method for performing approximate Bayesian inference when the likelihood function is intractable. In synthetic likelihood methods, the likelihood function is approximated parametrically via…
A spectral method is considered for approximating the fractional Laplacian and solving the fractional Poisson problem in 2D and 3D unit balls. The method is based on the explicit formulation of the eigenfunctions and eigenvalues of the…
We establish a new spectral inequality for the quantified estimation of the $H^s$-norm, $s\ge 0$ of a finite linear combination of eigenfunctions in a domain in terms of its $H^s$-norm in a strictly open subset of the whole domain. The…
In this paper, we prove sharp pointwise kernel estimates and dispersive properties for the linear wave equation on noncompact Riemannian symmetric spaces G/K of any rank with G complex. As a consequence, we deduce Strichartz inequalities…
We analyze certain bilinear forms involving $GL_3$ Kloosterman sums. As an application, we obtain an improved estimate for the $GL_3$ spectral large sieve inequality.
{We provide a probabilistic approach in order to investigate the smoothness of the solution to the Poisson and Dirichlet problems in $L$-shaped domains. In particular, we obtain (probabilistic) integral representations for the solution. We…
Extending a method of D. Wolke, we establish a general result on the large sieve with sparse sets S of moduli which are in a sense well-distributed in arithmetic progressions. We then apply our result to the case when S consists of sqares.…
We establish good numerical estimates for a certain class of integrals involving sixfold products of Bessel functions. We use relatively elementary methods. The estimates will be used in the study of a sharp Fourier restriction inequality…
In this paper various analytic techniques are com- bined in order to study the average of a product of a Hecke L- function and a symmetric square L-function at the central point in the weight aspect. The evaluation of the second main term…
The classical Grothendieck inequality is viewed as a statement about representations of functions of two variables over discrete domains by integrals of two-fold products of functions of one variable. An analogous statement is proved,…
The goal of this paper is to introduce a process that generates, given Hilbert space $H$ and symmetric operator $A$, an embedding of $H$ into an $L_2$-space through which $A$ is extended by a multiplication operator. This process will…
We prove a theorem that evaluates weighted averages of sums parametrised by congruence subgroups of $\operatorname{SL}_2(\mathbb{Z})$. In the proof, spectral methods are applied directly to the automorphic kernel instead of going over sums…
We prove sharp power-weighted strong type, weak type and restricted weak type inequalities for the heat and Poisson integral maximal operators, Riesz transform and a Littlewood-Paley type square function, emerging naturally in the harmonic…
The purpose of this article is to verify the conjectures of the previous paper in the particular case of $GL(4)$. We accomplish this in general, but observe two failures of the conjectures: First, that the Strong Interchange of Integrals…
A representation for the kernel of the transmutation operator relating the perturbed Bessel equation with the unperturbed one is obtained in the form of a functional series with coefficients calculated by a recurrent integration procedure.…
In this paper we establish some explicit and sharp estimates of the spectral gap and the log-Sobolev constant for mean field particles system, uniform in the number of particles, when the confinement potential have many local minimums. Our…
Sharp $L^p$ extensions of Pitt's inequality expressed as a weighted Sobolev inequality are obtained using convolution estimates and Stein-Weiss potentials. More generally, optimal constants are obtained for the full Stein-Weiss potential as…
This second paper of two companion papers on the estimation of power spectra specializes to the topic of estimating galaxy power spectra at large, linear scales using maximum likelihood methods. As in the first paper, the aims are…