Related papers: Moments from their very truncations
Power moments, modified moments, and optimized moments are powerful tools for solving microscopic models of macroscopic systems; however the expansion of the density of states as a continued fraction does not converge to the macroscopic…
Many mathematical statements have the following form. If something is true for all finite subsets of an infinite set $I$, then it is true for all of $I$. This paper describes some old and new results on infinite sets of linear and…
In this paper we approach the problem of perturbation from symmetry of strongly indefinite elliptic systems in dimension N>=3. We prove the existence of infinitely many solutions under suitable growth coinditions on the nonlinear terms.
This paper deals with the moment problem on a (not necessarily finitely generated) commutative unital real algebra $A$. We define moment functionals on $A$ as linear functionals which can be written as integrals over characters of $A$ with…
We will consider the indefinite truncated multidimensional moment problem. Necessary and sufficient conditions for a given truncated multisequence to have a signed representing measure $\mu$ with ${\rm card}\,{\rm supp}\, \mu$ as small as…
We first propose what we call the Gaussian Moments Conjecture. We then show that the Jacobian Conjecture follows from the Gaussian Moments Conjecture. We also give a counter-example to a more general statement known as the Moments Vanishing…
Several complementary approaches to investigate knotted solutions of Maxwell's equations in vacuum are now available in literature. However, only partial results towards a unified description of them have been achieved. This is potentially…
The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…
In the paper, the idea of describing not-yet-verified properties of quantum objects with logical many-valuedness is scrutinized. As it is argued, to promote such an idea, the following two foundational problems of many-valued quantum logic…
In this paper we consider two related objects: singular positive semidefinite Hankel block--matrices and associated degenerate truncated matrix Hamburger moment problems. The description of all solutions of a degenerate matrix Hamburger…
Using standard tools of harmonic analysis, we state and solve the problem of moments for non-negative measures supported on the unit ball of a Sobolev space of multivariate periodic trigonometric functions. We describe outer and inner…
In the History of Ideas, a succession of philosophical and scientific achievements, concerning the concept of space and its dimensionality, were essential to contribute, after a long period, to the theoretical possibility of thinking…
The identification of a solution to the dark matter problem has many arrows to its bow: if dark matter is a new elementary particle, both laboratory experiments and astrophysics can bring relevant and complementary pieces of information,…
Necessary and sufficient conditions for a measure to be an extreme point of the set of measures (on an abstract measurable space) with prescribed generalized moments are given, as well as an application to extremal problems over such moment…
We describe all solutions of the matrix Hamburger moment problem in a general case (no conditions besides solvability are assumed). We use the fundamental results of A.V. Shtraus on the generalized resolvents of symmetric operators. All…
The proper resolution of the so-called measurement problem requires a "top-down" conception of the quantum world that is opposed to the usual "bottom-up" conception, which builds on an intrinsically and maximally differentiated manifold.…
For the truncated moment problem associated to a complex sequence $\gamma ^{(2n)}=\{\gamma _{ij}\}_{i,j\in Z_{+},i+j \leq 2n}$ to have a representing measure $\mu $, it is necessary for the moment matrix $M(n)$ to be positive semidefinite,…
The quantum-mechanical description of the world, including human observers, makes substantial use of entanglement. In order to understand this, we need to adopt concepts of truth, probability and time which are unfamiliar in modern…
A broad set of sufficient conditions that guarantees the existence of the maximum entropy (maxent) distribution consistent with specified bounds on certain generalized moments is derived. Most results in the literature are either focused on…
According to modern quantum physics, at the microlevel, the dimension of space-time is at least 11; we only observe 4 dimensions because the others are compactified: the size along each of the other dimensions is much smaller than the…