Related papers: Subdifferential set of an operator
We study the decomposability and the subdifferential of the tensor nuclear norm. Both concepts are well understood and widely applied in matrices but remain unclear for higher-order tensors. We show that the tensor nuclear norm admits a…
Hyponormal operators are known to be among the most difficult operators to analyze. In this work, we focus on two finite types of hyponormal operators. The first type becomes analytic shifts, while the second type admits analytic models. A…
In this paper we introduce and prove some properties of $(\alpha;\beta)$-normal operators according to semi-Hilbertian space structures. Furthermore we s,ate various inequalities between the A-operator norm and A-numerical radius of…
In this paper, we study uniqueness problems for an entire function that shares small functions of finite order with their difference operators. In particular, we give a generalization of results in [2,3,13].
Nearly convex sets play important roles in convex analysis, optimization and theory of monotone operators. We give a systematic study of nearly convex sets, and construct examples of subdifferentials of lower semicontinuous convex functions…
We define and prove some properties of the semi-classical wavefront set. We also define and study semi-classical Fourier integral operators, of which we give a complete characterization. Lastly, we prove a generalization of the…
We show the existence of fundamental solutions for p-adic pseudo-differential operators with polynomial symbols.
In this paper we study the theory of operators on complex Hilbert spaces, which achieve the norm in the unit sphere. We prove important results concerning the characterization of the AN operators, see Definition 1.2. The class of AN…
For operators generated by a certain class of infinite band matrices with matrix elements we establish a characterization of the resolvent set in terms of polynomial solutions of the underlying higher order finite difference equations. This…
In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions…
A notion of resolvent set for an operator acting in a rigged Hilbert space $\D \subset \H\subset \D^\times$ is proposed. This set depends on a family of intermediate locally convex spaces living between $\D$ and $\D^\times$, called…
In this paper, we continue the analysis of the effects of semiclassical sub principal controlled quasimodes, approximate solutions to P(h)u(h,b), depending on the subprincipal symbol b, which can give spectral insta bility (pseudospectrum).…
The goal of this work is to characterize all second order difference operators of several variables that have discrete orthogonal polynomials as eigenfunctions. Under some mild assumptions, we give a complete solution of the problem.
We introduce the wave-front set for distributions with respect to Fourier images of weighted translation invariant Banach function spaces. We prove that usual mapping properties for pseudo-differential operators hold in the context of such…
An automorphism defined on an evolution algebra can provide both a finite number and an infinite number of evolution operators on it. This question is dealt with in the paper, as well as others more related to the evolution operators of…
We show that a point is solution of the Minty variational inequality of subdifferential type for a given function if and only if the function is increasing along rays starting from that point. This provides a characterization of the…
A complete classification of linear differential operators possessing finite-dimensional invariant subspace with a basis of monomials is presented.
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
We construct a set $M_d$ whose points parametrize families of Meixner polynomials in $d$ variables. There is a natural bispectral involution $b$ on $M_d$ which corresponds to a symmetry between the variables and the degree indices of the…
In this paper we study shorted operators relative to two different subspaces, for bounded operators on infinite dimensional Hilbert spaces. We define two notions of complementability in the sense of Ando for operators, and study the…