Related papers: Spherical Means and Pinned Distance Sets
In recent years, sparse spectral methods for solving partial differential equations have been derived using hierarchies of classical orthogonal polynomials on intervals, disks, disk-slices and triangles. In this work we extend the…
We give an upper bound for the weighted geometric mean using the weighted arithmetic mean and the weighted harmonic mean. We also give a lower bound for the weighted geometric mean. These inequalities are proven for two invertible positive…
We prove almost Strichartz estimates found after adding regularity in the spherical coordinates for Schr\"odinger-like equations. The estimates are sharp up to endpoints. The proof relies on estimates involving spherical averages. Sharpness…
The measurements with the background estimation from an off-zone are widely used in astrophysics, accelerator physics and other areas. Usually, the expected number of the background events in the off-zone and in the on-zone is known with a…
We present some old and new results on dispersive estimates for Schroedinger equations.
We show that the operator norm of an arbitrary bivariate polynomial, evaluated on certain spectral projections of spin operators, converges to the maximal value in the semiclassical limit. We contrast this limiting behavior with that of the…
We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…
We propose simple schemes that can perfectly identify projective measurement apparatus secretly chosen from a finite set. Entanglements are used in these schemes both to make possible the perfect identification and to improve the efficiency…
How can we analyze quantum correlations in large and noisy systems without quantum state tomography? An established method is to measure total angular momenta and employ the so-called spin-squeezing inequalities based on their expectations…
The Hausdorff distance is a measure of (dis-)similarity between two sets which is widely used in various applications. Most of the applied literature is devoted to the computation for sets consisting of a finite number of points. This has…
In this paper we give sharp norm estimates for the Bergman operator acting from weighted mixed-norm spaces to weighted Hardy spaces in the ball, endowed with natural norms.
In this article, we obtain several new weighted bounds for the numerical radius of a Hilbert space operator. The significance of the obtained results is the way they generalize many existing results in the literature; where certain values…
In this survey, we collect recent progress in the understanding of $L^{p}$ bounds for bilinear spherical averages and some associated maximal functions like the bilinear spherical maximal function and its lacunary counterpart. We describe…
We study the mutual information estimation for mixed-pair random variables. One random variable is discrete and the other one is continuous. We develop a kernel method to estimate the mutual information between the two random variables. The…
Order estimates for the Kolmogorov widths of an intersection of two finite-dimensional balls in a mixed norm under some conditions on the parameters are obtained.
This paper provides a survey of spherical designs and their applications, with a particular emphasis on the perspective of ``numerical analysis''. A set \(X_N\) of \(N\) points on the unit sphere \(\mathbb{S}^d\) is called a…
Spherical k-means is a widely used clustering algorithm for sparse and high-dimensional data such as document vectors. While several improvements and accelerations have been introduced for the original k-means algorithm, not all easily…
We provide Green's function estimates for parabolic operators on polyhedrons and polyhedral cones in $\mathbb{R}^3$. These estimates incorporate mixed weights, which include appropriate powers of the distances to the vertices, the edges,…
We employ the framework of operational calculus to derive the operators associated with the spherical mean and a class of related averaging means of a function in $n$-dimensional space. Beginning with the classical definition of the…
In this paper we present an extension of known semidefinite and linear programming upper bounds for spherical codes and consider a version of this bound for distance graphs. We apply the main result for the distance distribution of a…