Related papers: Laurent polynomial moment problem: a case study
In this paper, we consider a problem of Lang about finiteness of torsion points on plane rational curves over $\mathbb C$, and prove some results towards a matrix analogue of this problem.
By introducing a kind of special functions namely exponent-like function, cosine-like function and sine-like function, we obtain explicitly the basic structures of solutions of initial value problem at the original point for this kind of…
We study the truncated multidimensional moment problem with a general type of truncations. The operator approach to the moment problem is presented. A way to construct atomic solutions of the moment problem is indicated.
Motivated by polynomial approximations of differential forms, we study analytical and numerical properties of a polynomial interpolation problem that relies on function averages over interval segments. The usage of segment data gives rise…
Let $X$ be a finite set in $Z^d$. We consider the problem of optimizing linear function $f(x) = c^T x$ on $X$, where $c\in Z^d$ is an input vector. We call it a problem $X$. A problem $X$ is related with linear program $\max\limits_{x \in…
We give a simple proof of the moment-indeterminacy of the sequence $(n!)^t$ for $t > 2,$ using Lin's condition. Under a logarithmic self-decomposability assumption, the method conveys to power sequences defined as the rising factorials of a…
Non-commutative polynomial optimization is a powerful technique with numerous applications in quantum nonlocality, quantum key distribution, causal inference, many-body physics, amongst others. The standard approach is to reduce such…
We consider the $*$-Markov equation for the symmetric Laurent polynomials in three variables with integer coefficients, which is an equivariant analog of the classical Markov equation for integers. We study how the properties of the Markov…
We study a Dirichlet problem driven by the (degenerate or singular) fractional $p$-Laplacian and involving a $(p-1)$-superlinear reaction at infinity, not necessarily satisfying the Ambrosetti-Rabinowitz condition. Using critical point…
In this paper we study the truncated power moment problem with an odd number of prescribed moments. A Nevanlinna-type formula is derived for this moment problem in the case when the moment problem has more than one solution (the…
The singularity confinement test is very useful for isolating integrable cases of discrete-time dynamical systems, but it does not provide a sufficient criterion for integrability. Quite recently a new property of the bilinear equations…
The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…
In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…
We develop a combinatorial model of the associated Hermite polynomials and their moments, and prove their orthogonality with a sign-reversing involution. We find combinatorial interpretations of the moments as complete matchings, connected…
This paper considers the question of P = NP in context of the polynomial time SAT algorithm. It posits proposition dependent on existence of conjectured problem that even where the algorithm is shown to solve SAT in polynomial time it…
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…
A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the…
We introduce the concept of reflexive moment functional in two variables and the definition of reflexive orthogonal polynomial system. Also reverse matrices and their interesting algebraic properties are studied. Reverse matrices and…
The Lambert $W$ function, giving the solutions of a simple transcendental equation, has become a famous function and arises in many applications in combinatorics, physics, or population dyamics just to mention a few. In the last decade it…
Using, as main tool, the convergence theorem for discrete martingales and the mean value property of harmonic functions we solve, a particular case of, Dirichlet problem.