Related papers: Linear first order differential operators and thei…
Let $T$ be an absolutely continuous polynomially bounded operator, and let $\theta$ be a singular inner function. It is shown that if $\theta(T)$ is invertible and some additional conditions are fulfilled, then $T$ has nontrivial…
We study invariant operators in general tensor models. We show that representation theory provides an efficient framework to count and classify invariants in tensor models. In continuation and completion of our earlier work, we present two…
Let $T:D(T)\rightarrow H_2$ be a densely defined closed operator with domain $D(T)\subset H_1$. We say $T$ to be absolutely minimum attaining if for every closed subspace $M$ of $H_1$, the restriction operator $T|_M:D(T)\cap M\rightarrow…
A systematic exposition is given of the theory of invariant differential operators on a not necessarily reductive homogeneous space. This exposition is modelled on Helgason's treatment of the general reductive case and the special…
In this paper the notion of an M-th order invariant bilinear differential pairing is introduced and a formal definition is given. If the manifold has an AHS structure, then various first order pairings are constructed. This yields a…
Representations of coherent state Lie algebras on coherent state manifolds as first order differential operators are presented. The explicit expressions of the differential action of the generators of semisimple Lie groups determine for…
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…
This paper develops some deeper consequences of an extended definition, proposed previously by the author, of pseudo-differential operators that are of type $1,1$ in H\"ormander's sense. Thus, it contributes to the long-standing problem of…
In this paper, we consider the first order Hardy inequalities using simple equalities. This basic setting not only permits to derive quickly many well-known Hardy inequalities with optimal constants, but also supplies improved or new…
The aim of this paper is to bring into the picture a new phenomenon in the theory of orthogonal matrix polynomials satisfying second order differential equations. The last few years have witnessed some examples of a (fixed) family of…
The Koopman operator provides a linear perspective on non-linear dynamics by focusing on the evolution of observables in an invariant subspace. Observables of interest are typically linearly reconstructed from the Koopman eigenfunctions.…
Monotone operators, especially in the form of subdifferential operators, are of basic importance in optimization. It is well known since Minty, Rockafellar, and Bertsekas-Eckstein that in Hilbert space, monotone operators can be understood…
We consider equivariant continuous families of discrete one-dimensional operators over arbitrary dynamical systems. We introduce the concept of a pseudo-ergodic element of a dynamical system. We then show that all operators associated to…
In this paper, we establish a condition on the coefficients of differential operators generated in the space of square-integrable functions on the entire real line by an ordinary differential expression with periodic, complex-valued…
In this paper, we study scalar the forth order linear differential operators over an oriented 2-dimensional manifold. We investigate differential invariants of these operators and show their application to the equivalence problem.
In our another recent article, we introduce a new dynamical property for linear operators called norm-unimodality which implies distributional chaos. In the present paper, we'll give a further discussion of norm-unimodality. It is showed…
The simplest and most natural examples of completely nonunitary contractions on separable complex Hilbert spaces which have polynomial characteristic functions are the nilpotent operators. The main purpose of this paper is to prove the…
Let us denote ${\cal V}$, the finite dimensional vector spaces of functions of the form $\psi(x) = p_n(x) + f(x) p_m(x)$ where $p_n(x)$ and $p_m(x)$ are arbitrary polynomials of degree at most $n$ and $m$ in the variable $x$ while $f(x)$…
This article introduces several new relations among related Hilbert space operators. In particular, we prove some L\"{o}ewner partial orderings among $T, |T|, \mathcal{R}T, \mathcal{I}T, |T|+|T^*|$ and many other related forms, as a new…
This paper grew out of the author's work on arXiv:2504.18460. Differential operators in the sense of Grothendieck acting between modules over a commutative ring can be interpreted as torsion elements in the bimodule of all operators with…