Related papers: Multivariate transforms of total positivity
This paper deals with representing in concrete fashion those Hilbert spaces that are vector subspaces of the Hardy spaces $H^p(\bb D^n) \ (1\le p\le \infty)$ that remain invariant under the action of coordinate wise multiplication by an…
We consider kernels of discrete convolution operators or, equivalently, homogeneous solutions of partial difference operators and show that these solutions always have to be exponential polynomials. The respective polynomial space in…
Conditions for linear integral operators on $L_p$ over measure spaces to satisfy the polynomial covariance type commutation relations are described in terms of defining kernels of the corresponding integral operators. Representation by…
Several new transformations for q-binomial coefficients are found, which have the special feature that the kernel is a polynomial with nonnegative coefficients. By studying the group-like properties of these positivity preserving…
Kendall transformation is a conversion of an ordered feature into a vector of pairwise order relations between individual values. This way, it preserves ranking of observations and represents it in a categorical form. Such transformation…
Representations of polynomial covariance type commutation relations by linear integral operators on $L_p$ over measures spaces are investigated. Necessary and sufficient conditions for integral operators to satisfy polynomial covariance…
Let $X$ be a nonempty set, and let $\mathcal{T}_X$ be the full transformation semigroup on $X$. For a partition $\mathcal{P} = \{X_i \;|\; i\in I\}$ of $X$, we consider the semigroup $T(X, \mathcal{P}) = \{f\in \mathcal{T}_X\;|\; \forall…
Representations by linear integral operators on $L_p$ spaces over measure spaces are investigated for the polynomial covariance type commutation relations and more general two-sided generalizations of covariance commutation relations…
In this paper, we investigate the trigonometric Heckman-Opdam polynomials of type $A_1$. We establish connections with ultraspherical polynomials and derive an explicit expression for the associated Poisson kernel. Using the product…
We introduce the notion of order-preserving multi-homogeneous mapping which allows to study Perron-Frobenius type theorems and nonnegative tensors in unified fashion. We prove a weak and strong Perron-Frobenius theorem for these maps and…
In 1990, J.L. Krivine introduced the notion of storage operator to simulate "call by value" in the "call by name" strategy. J.L. Krivine has shown that, using G\"odel translation of classical into intuitionitic logic, we can find a simple…
Given a pair of finite posets $A \subseteq P$, the function counting integer-valued order preserving extensions of an order preserving map $\lambda : A\rightarrow \mathbb{Z}$ from $A$ to $P$ is given by a piecewise polynomial in $\lambda$.…
We study multivariate linear tensor product problems with some special properties in the worst case setting. We consider algorithms that use finitely many continuous linear functionals. We use a unified method to investigate tractability of…
We consider positive semidefinite kernels valued in the $*$-algebra of adjointable operators on a VE-space (Vector Euclidean space) and that are invariant under actions of $*$-semigroups. A rather general dilation theorem is stated and…
Given a polynomial P of partial derivatives of the Kahler metric, expressed as a linear combination of directed multigraphs, we prove a simple criterion in terms of the coefficients for $P$ to be an invariant polynomial, i.e. invariant…
In this paper we investigate the class of invariant positive definite kernels on the free semigroup on N generators. We provide a combinatorial description of the positivity of the kernel in terms of Dyck paths and then we find a…
We consider positive semidefinite kernels which have values given by bounded linear operators on certain bundles of Hilbert spaces and which are invariant under actions of $*$-semigroupoids. For these kernels, we prove that there exist…
We derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be…
Precision tests of the Standard Model and searches for beyond the Standard Model physics often require nuclear structure input. There has been a tremendous progress in the development of nuclear ab initio techniques capable of providing…
In this paper we continue to investigate a certain class of Hankel-like positive definite kernels using their associated orthogonal polynomials. The main result of this paper is about the structure of this kind of kernels.