Related papers: On Positivity Preservers with constant Coefficient…
Kantor and Trishin described the algebra of polynomial invariants of the adjoint representation of the Lie supergalgebra $gl(m|n)$ and a related algebra $A_s$ of what they called pseudosymmetric polynomials over an algebraically closed…
Deciding the positivity of a sequence defined by a linear recurrence and initial conditions is, in general, a hard problem. When the coefficients of the recurrences are constants, decidability has only been proven up to order 5. The…
We study the total positivity of the kernel $1/(x^2 + 2 \cos(\pi\a)xy +y^2).$ The case of infinite order is characterized by an application of Schoenberg's theorem. We then give necessary conditions for the cases of any given finite order…
We consider linear recurrences with polynomial coefficients of Poincar\'e type and with a unique simple dominant eigenvalue. We give an algorithm that proves or disproves positivity of solutions provided the initial conditions satisfy a…
This paper defines the notion of generators for a class of decreasing radial Loewner chains which are only continuous with respect to time. For this purpose, "Loewner's integral equation" which generalizes Loewner's differential equation is…
In this work we examine quantum states which have non-negative amplitudes (in a fixed basis) and the channels which preserve them. These states include the ground states of stoquastic Hamiltonians and they are of interest since they avoid…
The composition operators preserving total non-negativity and total positivity for various classes of kernels are classified, following three themes. Letting a function act by post composition on kernels with arbitrary domains, it is shown…
We consider generators of positive $C_0$-semigroups and, more generally, resolvent positive operators $A$ on ordered Banach spaces and seek for conditions ensuring the negativity of their spectral bound $s(A)$. Our main result characterizes…
Belton-Guillot-Khare-Putinar [J. d'Analyse Math. 2023] classified the post-composition operators that preserve TP/TN kernels of each specified order. We explain how to extend this from preservers to transforms, and from one to several…
A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…
We develop a systematic theory of eventually positive semigroups of linear operators mainly on spaces of continuous functions. By eventually positive we mean that for every positive initial condition the solution to the corresponding Cauchy…
Let a and b be non-zero rational numbers that are multiplicatively independent. We study the natural density of the set of primes p for which the subgroup of the multiplicative group of the finite field with p elements generated by (a\mod…
Ito's construction of Markovian solutions to stochastic equations driven by a L\'evy noise is extended to nonlinear distribution dependent integrands aiming at the effective construction of linear and nonlinear Markov semigroups and the…
Characterizing in a constructive way the set of real functions whose Fourier transforms are positive appears to be yet an open problem. Some sufficient conditions are known but they are far from being exhaustive. We propose two constructive…
We consider time-changed diffusions driven by generators with discontinuous coefficients. The PDE's connections are investigated and in particular some results on the asymptotic analysis according to the behaviour of the coefficients are…
Let $U$ be an open set of $\mathbb{R}^n$, $m$ a positive Radon measure on $U$ such that ${\rm supp}[m]=U$, and $(P_t)_{t>0}$ a strongly continuous contraction sub-Markovian semigroup on $L^2(U;m)$. We investigate the structure of…
We define discrete generating series for arbitrary functions \( f \colon \mathbb{Z}^n \rightarrow \mathbb{C} \) and derive functional relations that these series satisfy. For linear difference equations with constant coefficients, we…
If G is a finitely generated powerful pro-p group satisfying a certain law v=1, and if G can be generated by a normal subset T of finite width which satisfies a positive law, we prove that G is nilpotent. Furthermore, the nilpotency class…
A real sequence $(a_k)_{k=0}^\infty$ is called {\it totally positive} if all minors of the infinite Toeplitz matrix $ \left\| a_{j-i} \right\|_{i, j =0}^\infty$ are nonnegative (here $a_k=0$ for $k<0$). In this paper, which continues our…
A regular factor is a factor algebra of the unitriangular Lie algebra with respect to some regular ideal. In the paper we construct system of generators of the field of invariants for the coadjoint representation of an arbitrary regular…