Related papers: A Decomposition for Hardy Martingales III

A brief proof of Lie's classification of finite dimensional subalgebras of vector fields on the complex plane that have a proper Levi decomposition is given. The proof uses basic representation theory of sl(2, C). This, combined with…

In this paper, we not only give the extensions of the results given in [7] by Gill et al. for log-convex functions, but also obtain some new Hadamard type inequalities for log-convex, m-convex and (alpha,m)-convex functions.

The Helmholtz decomposition splits a sufficiently smooth vector field into a gradient field and a divergence-free rotation field. Existing decomposition methods impose constraints on the behavior of vector fields at infinity and require…

We prove a version of Rao decomposition for quasi-martingales indexed by a linearly ordered set.

Filter convergence of vector lattice-valued measures is considered, in order to deduce theorems of convergence for their decompositions. First the $\sigma$-additive case is studied, without particular assumptions on the filter; later the…

Let $p(\cdot)$ be a measurable function defined on a probability space satisfying $0<p_-:={\rm ess}\inf_{x\in \Omega}p(x)\leq {\rm ess}\sup_{x\in\Omega}p(x)=:p_+<\infty$. We investigate five types of martingale Hardy spaces $H_{p(\cdot)}$…

We prove descent theorems for semiorthogonal decompositions using techniques from derived algebraic geometry. Our methods allow us to capture more general filtrations of derived categories and even marked filtrations, where one descends not…

We present an elementary treatment of the Optional Decomposition Theorem for continuous semimartingales and general filtrations. This treatment does not assume the existence of equivalent local martingale measure(s), only that of strictly…

We shall present an elementary approach to extremal decompositions of (quantum) covariance matrices determined by densities. We give a new proof on former results and provide a sharp estimate of the ranks of the densities that appear in the…

We propose a new hypermatrix singular value decomposition based upon the spectral decomposition of the symmetric products of transposes.

We analytically solve Poisson's equation for the magnetic scalar potential generated by a uniformly magnetized rectangular prism and determine a closed-form solution for the magnetic scalar potential given only in terms of arctan and…

We take matrix decompositions that are usually applied to matrices over the real numbers or complex numbers, and extend them to matrices over an algebra called the double numbers. In doing so, we unify some matrix decompositions: For…

We prove local refined versions of Hardy's and Rellich's inequalities as well as of uncertainty principles for sums of squares of vector fields on bounded sets of smooth manifolds under certain assumptions on the vector fields. We also give…

We show that a twist of a three-dimensional tube of uniform cross-section yields an improved decay rate for the heat semigroup associated with the Dirichlet Laplacian in the tube. The proof employs Hardy inequalities for the Dirichlet…

This paper considers a way of generalizing the t-SVD of third-order tensors (regarded as tubal matrices) to tensors of arbitrary order N (which can be similarly regarded as tubal tensors of order (N-1)). \color{black}Such a generalization…

This note studies the Hardy-type inequalities for vector fields with the $L^1$ norm of the $\curl$. In contrast to the well-known results in the whole space for the divergence-free vectors, we generalize the Hardy-type inequalities to the…

The main purpose of this article is to provide an alternate proof to a result of Perelman on gradient shrinking solitons. In dimension three we also generalize the result by removing the $\kappa$-non-collapsing assumption. In high dimension…

The decomposability of a Cartesian product of two nondecomposable manifolds into products of lower dimensional manifolds is studied. For 3-manifolds we obtain an analog of a result due to Borsuk for surfaces, and in higher dimensions we…

This is a continuation of the work initiated in a previous paper on so-called driven cofactor systems, which are partially decoupling second-order differential equations of a special kind. The main purpose in that paper was to obtain an…

This paper defines local weighted Hardy spaces with variable exponent. Local Hardy spaces permit atomic decomposition, which is one of the main themes in this paper. A consequence is that the atomic decomposition is obtained for the…