Related papers: Linear operators preserving volume polynomials
A complete characterisation is given of all the linear isometries of the Fr\'echet space of all holomorphic functions on the unit disc, when it is given one of the two standard metrics: these turn out to be weighted composition operators of…
Given a Banach space $X$ and $d\in \mathbb{N}$, we construct a metric space $\mathbb{V}_X^d$ with the property that every $d$-homogeneous polynomial defined on $X$ factors through a Lipschitz map on it. We prove that the metric on…
We prove a characterization of the dual mixed volume in terms of functional properties of the polynomial associated to it. To do this, we use tools from the theory of multilinear operators on spaces of continuos functions. Along the way we…
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…
In this paper, the boundedness of some sublinear operators is proved on homogeneous Herz-Morrey spaces with variable exponent.
It is known that a linear system with a system matrix A constitutes a Hamiltonian system with a quadratic Hamiltonian if and only if A is a Hamiltonian matrix. This provides a straightforward method to verify whether a linear system is…
In a first objective we improve our understanding about surjective and bijective bounded linear operators preserving orthogonality from a JB$^*$-algebra $\mathcal{A}$ into a JB$^*$-triple $E$. Among many other conclusions, it is shown that…
We demonstrate a method of associating the principal symbol at a $K$-point with a linear differential operator acting between modules over a commutative algebra, and we use it to define the ellipticity of a linear differential operator in a…
We prove that linearizing certain families of polynomial optimization problems leads to new functorial operations in real convex sets. We show that under some conditions these operations can be computed or approximated in ways amenable to…
We prove that the super-linearizability of polynomial systems is preserved by all currently known classes of polynomial automorphisms of $\R^n$. We then establish connections between such automorphisms and a sufficient condition for…
We investigate a linear operator associated with a functional equation that arises from studying some class of invariant measures under multidimensional transformations. By examining its iterates, we derive an explicit solution formula for…
For a locally compact abelian group $\textbf{R}$ with a uniform lattice $\Lambda$ and a group $G$ that acts on $\textbf{R}$ by continuous automorphisms, we study operators commuting with the representation of $G \rtimes \Lambda$ on…
In this paper we present how spectral properties of certain linear operators vary when operators are considered in different Hilbert spaces having common dense domain as the space of polynomials in one real variable with complex…
Given a sequence of polynomials $(p_n)_n$, an algebra of operators $\mathcal A$ acting in the linear space of polynomials and an operator $D_p\in \mathcal A$ with $D_p(p_n)=\theta_np_n$, where $\theta_n$ is any arbitrary eigenvalue, we…
Representations of polynomial covariant type commutation relations by pairs of linear integral operators and multiplication operators on Banach spaces $L_p$ are constructed.
Unlike the classical polynomial case there has not been invented up to very recently a tool similar to the Bernstein-Bezier representation which would allow us to control the behavior of the exponential polynomials. The exponential analog…
In this article we discuss the solvability of some class of fully nonlinear equations, and equations with p-Laplacian in more general conditions by using a new approach given in [1] for studying the nonlinear continuous operator. Moreover…
We prove that Burenkov's Extension Operator preserves Sobolev spaces built on general Morrey spaces, including classical Morrey spaces. The analysis concerns bounded and unbounded open sets with Lipschitz boundaries in the n-dimensional…
We study the effect of linear transformations on quantum fields with applications to vertex operator presentations of symmetric functions. Properties of linearly transformed quantum fields and corresponding transformations of…
Conditions guaranteeing convergence of linear stochastic Volterra operators are studied. Necessary and sufficient conditions for mean square convergence are established, while almost sure convergence of the linear operator is shown to imply…