Related papers: A differential operator representation of continuo…
Every diagonalmatrix D yields an endomorphism on the n-dimensional complex vectorspace. If one provides this space with Hoelder norms, we can compute the operator norm of D. We define homogeneous weighted spaces as a generalization of…
In this paper, we study the differentiation operator acting on discrete function spaces; that is spaces of functions defined on an infinite rooted tree. We discuss, through its connection with composition operators, the boundedness and…
We obtaine the full characterization of proper closed invariant subspaces of a generalized backward shift operator (Pommiez operator) in the Frechet space of all holomorphic functions on a simply connected domain $\Omega$ of the complex…
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…
In this note we study the structure of shift-preserving operators acting on a finitely generated shift-invariant space. We define a new notion of diagonalization for these operators, which we call s-diagonalization. We give necessary and…
This chapter uses categorical techniques to describe relations between various sets of operators on a Hilbert space, such as self-adjoint, positive, density, effect and projection operators. These relations, including various…
We study topological boundedness of order-to-topology bounded and order-to-topology continuous operators from ordered vector spaces to topological vector spaces. The uniform boundedness principle for such operators is investigated.
We characterize when the level sets of a continuous quasi-monotone functional defined on a suitable convex subset of a normed space can be uniquely represented by a family of bounded continuous functionals. Furthermore, we investigate how…
We study strongly continuous and locally equicontinuous families of operators on sequentially complete Hausdorff locally convex spaces. In case of Saks spaces, we relate the general notions to bi-continuity as well as equitightness. In this…
This paper establishes various variational properties of parametrized versions of two convexity-preserving constructs that were recently introduced in the literature: the proximal composition of a function and a linear operator, and the…
It is proved that every linear biseparating map between spaces of vector-valued differentiable functions is a weighted composition map. As a consequence, such a map is always continuous.
The new notion of operator/matrix $k$-tone functions is introduced, which is a higher order extension of operator/matrix monotone and convex functions. Differential properties of matrix $k$-tone functions are shown. Characterizations,…
We address a linearity problem for differentiable vectors in representations of infinite-dimensional Lie groups on locally convex spaces, which is similar to the linearity problem for the directional derivatives of functions.
We characterize all natural linear operations between spaces of differential forms on contact manifolds. Our main theorem says roughly that such operations are built from some algebraic operators which we introduce and the exterior…
Differential chains are a proper subspace of de Rham currents given as an inductive limit of Banach spaces endowed with a geometrically defined strong topology. Boundary is a continuous operator, as are operators that dualize to Hodge star,…
We consider a tensor product of two spaces of holomorphic functions on a Hermitian symmetric space of tube type. Then generically this is decomposed into a direct sum of irreducible subrepresentations. In this manuscript, we construct the…
The concept of proximate order is widely used in the theories of entire, meromorphic, subharmonic and plurisubharmonic functions. We give a general interpretation of this concept as a proximate growth function relative to a model growth…
We propose a definition of differential operators of an associative algebra $A$ in the spirit of Hochschild cohomology. Specifically we define $D(A)$ as the zero cohomology of a certain bicomplex formed by Hom-spaces…
The interaction between discrete and continuous mathematics lies at the heart of many fundamental problems in applied mathematics and computational sciences. In this paper we discuss the problem of discretizing vector-valued functions…
INTRODUCTION This papers deals with partial differential equations of second order, linear, with constant and not constant coefficients, in two variables, which admit real characteristics. I face the study of PDEs with the mentality of the…