Related papers: Infinite dimensional moment problem: open question…
Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.
In the last years many results in the area of semidefinite programming were obtained for invariant (finite dimensional, or infinite dimensional) semidefinite programs - SDPs which have symmetry. This was done for a variety of problems and…
The aim of this paper is to study the full $K-$moment problem for measures supported on some particular non-linear subsets $K$ of an infinite dimensional vector space. We focus on the case of random measures, that is $K$ is a subset of all…
Uncertainty relations are usually stated as bounds on selected combinations of variances, but the full covariance matrix contains substantially richer information about the geometry of quantum state space and about the operational…
Position-momentum entanglement is a versatile high-dimensional resource in quantum optics. From fundamental tests of reality, to application in quantum technologies, spatial entanglement has had an increasing growth in recent years. In this…
We investigate metric projections and distance functions referring to convex bodies in finite-dimensional normed spaces. For this purpose we identify the vector space with its dual space by using, instead of the usual identification via the…
The aim of this paper is to clear up the problem of the connection between the 3D geometric moments invariants and the invariant theory, considering a problem of describing of the 3D geometric moments invariants as a problem of the…
The quest to reveal the physical essence of the infinitely many symmetries and conservation laws that are intrinsic to integrable systems has historically posed a significant challenge at the confluence of physics and mathematics. This…
The theory of holomorphic functions of several complex variables is applied in proving a multidimensional variant of a theorem involving an exponential boundedness criterion for the classical moment problem. A theorem of Petersen concerning…
With any convex function F on a finite-dimensional linear space X such that F goes to infinity at infinity, we associate a Borel measure on the dual space X*. This measure is obtained by pushing forward the measure exp(-F(x))dx under the…
A quantum-mechanical system comes naturally equipped with a convex space: each (Hermitian) operator has a (real) expectation value, and the expectation value of the square any Hermitian operator must be non-negative. This space is of…
We introduce the notion of almost finite dimensionality of algebras and study its connection with the classical finiteness conditions.
Complex moment sequences are exactly those which admit positive definite extensions on the integer lattice points of the upper diagonal half-plane. Here we prove that the aforesaid extension is unique provided the complex moment sequence is…
The field of two-dimensional topological semimetals, which emerged at the intersection of two-dimensional materials and topological materials, have been rapidly developing in recent years. In this article, we briefly review the progress in…
This paper begins the study of infinite-dimensional modules defined on bicomplex numbers. It generalizes a number of results obtained with finite-dimensional bicomplex modules. The central concept introduced is the one of a bicomplex…
This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of…
In this paper several examples of gaps (lacunes) between dimensions of maximal and submaximal symmetric models are considered, which include investigation of number of independent linear and quadratic integrals of metrics and counting the…
Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate…
A geometric mechanism that may, in analogy to similar notions in physics, be considered as "symmetry breaking" in geometry is described, and several instances of this mechanism in differential geometry are discussed: it is shown how…
Preliminary results of our investigations on solving indefinite qua\-dra\-tic programs by dynamical systems are given. First, dynamical systems corresponding to two fundamental DC programming algorithms to deal with indefinite quadratic…