Related papers: Packing measures and dimensions on cartesian produ…
In this note, we obtain a full characterization of radial Carleson measures for the Hilbert-Hardy space on tube domains over symmetric cones. For large derivatives, we also obtain a full characterization of the measures for which the…
A given Hamiltonian matrix H with real spectrum is assumed tridiagonal and non-Hermitian. Its possible Hermitizations via an amended, ad hoc inner-product metric are studied. Under certain reasonable assumptions, all of these metrics are…
We establish variation and oscillation inequalities for convolution products of probability measures on Z.
During the last few years several new results on packing problems were obtained using a blend of tools from semidefinite optimization, polynomial optimization, and harmonic analysis. We survey some of these results and the techniques…
Pointwise tangential dimensions are introduced for metric spaces. Under regularity conditions, the upper, resp. lower, tangential dimensions of X at x can be defined as the supremum, resp. infimum, of box dimensions of the tangent sets, a…
The choice of a star product realization for noncommutative field theory can be regarded as a gauge choice in the space of all equivalent star products. With the goal of having a gauge invariant treatment, we develop tools, such as…
A novel solution to the quantum measurement problem is presented by using a new asymmetric equation that is complementary to the Schr\"odinger equation. Solved for the hydrogen atom, the new equation describes the temporal and spatial…
The use of unitary invariant subspaces of a Hilbert space $\mathcal{H}$ is nowadays a recognized fact in the treatment of sampling problems. Indeed, shift-invariant subspaces of $L^2(\mathbb{R})$ and also periodic extensions of finite…
We study dimensions of strange non-chaotic attractors and their associated physical measures in so-called pinched skew products, introduced by Grebogi and his coworkers in 1984. Our main results are that the Hausdorff dimension, the…
Recent studies have identified materials and devices whose behavior lies beyond the scope of conventional electronic-structure theory. Such theories are formulated entirely in terms of Hamiltonian evolution and therefore describe only…
One of the goals of this article is to define a an unified setting adapted to the description of means (normalized integrals or invariant means) on an infinite product of measured spaces with infinite measure. We first remark that some…
The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…
We propose and study a novel collection of signed measures, which will be apply called Taylor measures. Stochastic versions of the new measures are also defined and studied. We illustrate, through examples, how the deterministic and…
In geometry, there are several challenging problems studying numbers associated to convex bodies. For example, the packing density problem, the kissing number problem, the covering density problem, the packing-covering constant problem,…
In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…
Weak values and measurements have been proposed as means to achieve dramatic enhancements in metrology based on the greatly increased range of possible measurement outcomes. Unfortunately, the very large values of measurement outcomes occur…
The space of $G$-invariant metrics on a homogeneous space $G/H$ is in one-to-one correspondence with the set of inner products on the tangent space $\fr{m}\cong T_{{\it o}}(G/H)$, which are invariant under the isotropy representation. When…
We present a detailed study of the curvature and symplectic asphericity properties of symmetric products of surfaces. We show that these spaces can be used to answer nuanced questions arising in the study of closed Riemannian manifolds with…
We extend some of the measures of association defined by Lazarsfeld and Martin, obtaining useful invariants to compare the birational geometry of two varieties having different dimensions. We explore such invariants providing examples and…
Let $L$ be a holomorphic line bundle on a compact complex manifold $X$ of dimension $n,$ and let $e^{-\phi}$ be a continuous metric on $L.$ Fixing a measure $d\mu$ on $X$ gives a sequence of Hilbert spaces consisting of holomorphic sections…