Related papers: Total positivity of a Cauchy kernel
We consider the Cauchy problem for the hyperbolic-elliptic Ishimori system with general decoupling constant $\kappa \in \mathbb{R}$ and prove global well-posedness in the critical Sobolev space. The proof relies primarily on new bilinear…
We introduce a new class of combinatorial objects, named tight gradings, which are certain nonnegative integer-valued functions on maximal Dyck paths. Using tight gradings, we derive a manifestly positive formula for any wall-function in a…
We study how iterated and composed completely positive maps act on operator-valued kernels. Each kernel is realized inside a single Hilbert space where composition corresponds to applying bounded creation operators to feature vectors. This…
We show that properties of pairs of finite, positive and regular Borel measures on the complex unit circle such as domination, absolute continuity and singularity can be completely described in terms of containment and intersection of their…
We define a hierarchy of systems with topological completely positive entropy in the context of continuous countable amenable group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the…
We consider a finite system $\{X_1, X_2, \ldots, X_n\}$ of complete vector fields acting on smooth manifolds $M$ equipped with a smooth positive measure. We assume that the system satisfies H\"ormander's condition and generates a finite…
The estimates of the uniform norm of the Chebyshev polynomials associated with a compact set $K$ in the complex plane are established. These estimates are exact (up to a constant factor) in the case where $K$ consists of a finite number of…
The estimates of the uniform norm of the Chebyshev polynomial associated with a compact set $K$ consisting of a finite number of continua in the complex plane are established. These estimates are exact (up to a constant factor) in the case…
Let $A$ be a subset of primes up to $x$. If we assume $A$ is well-distributed (in the Siegel-Walfisz sense) in any arithmetic progressions to moduli $q\leqslant(\log x)^c$ for any $c>0$, then the sumset $A+A$ has density 1/2 in the natural…
The existence and multiplicity of positive periodic solutions for second order non-autonomous singular dynamical systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. Our…
We present a characterization for the continuous, isotropic and positive definite kernels on a product of spheres along the lines of a classical result of I. J. Schoenberg on positive definiteness on a single sphere. We also discuss a few…
We investigate the interaction between the existence of reproducing kernels on infinite-dimensional Hermitian vector bundles and the positivity properties of the corresponding bundles. The positivity refers to the curvature form of certain…
The main aim of this paper is to establish a deep link between the totally nonnegative grassmannian and the quantum grassmannian. More precisely, under the assumption that the deformation parameter $q$ is transcendental, we show that…
Building on work by Kontsevich, Soibelman, Nagao and Efimov, we prove the positivity of quantum cluster coefficients for all skew-symmetric quantum cluster algebras, via a proof of a conjecture first suggested by Kontsevich on the purity of…
A combinatorial property of prositive group presentations, called completeness, is introduced, with an effective criterion for recognizing complete presentations, and an iterative method for completing an incomplete presentation. We show…
Guralnick, Kunyavskii, Plotkin and Shalev have shown that the solvable radical of a finite group $G$ can be characterized as the set of all $x\in G$ such that $<x,y>$ is solvable for all $y\in G$. We prove two generalizations of this…
Let $\chi(x)\in \mathbb{Z}[x]$ be a monic polynomial whose roots are distinct integers. We study the ideal class monoid and the ideal class group of the ring $\mathbb{Z}[x]/(\chi(x))$. We obtain formulas for the orders of these objects, and…
We use the kernel category to give a finiteness condition for semigroups. As a consequence we provide yet another proof that finitely generated periodic semigroups of matrices are finite.
We consider complete positivity of dynamics regarding subsystems of an open composite quantum system, which is subject of a completely positive dynamics. By "completely positive dynamics", we assume the dynamical maps called the completely…
Let $E \subset \mathbb R^d$, $d \ge 2$, be compact, and let $\phi(x,y)$ be a smooth function satisfying the Phong--Stein rotational curvature condition on $\{\phi(x,y)=1\}$. We prove that if $\dim_{\mathcal H}(E)>1$, then $$…