Related papers: Dynamics of unbounded linear operators

We solve a number of questions pertaining to the dynamics of linear operators on Hilbert spaces, sometimes by using Baire category arguments and sometimes by constructing explicit examples. In particular, we prove the following results. - A…

We propose a theory of linear differential equations driven by unbounded operator-valued rough signals. As an application we consider rough linear transport equations and more general linear hyperbolic symmetric systems of equations driven…

We introduce a class of linear bounded invertible operators on Banach spaces, called shift operators, which comprises weighted backward shifts and models finite products of weighted backward shifts and dissipative composition operators. We…

We prove H\"older continuity up to the boundary for solutions of quasi-linear degenerate elliptic problems in divergence form, not necessarily of variational type, on Lipschitz domains with Neumann and Robin boundary conditions. This…

Extending previous results of Bourdon and Shapiro we characterize the hypercyclic and mixing composition operators $C_{\varphi}$ for the automorphisms of $\mathbb{D}$ on any of the spaces $H^{p}$ with $1\leqslant p<+\infty$.

Given a linear semi-bounded symmetric operator $S\ge -\omega$, we explicitly define, and provide their nonlinear resolvents, nonlinear maximal monotone operators $A_\Theta$ of type $\lambda>\omega$ (i.e. generators of one-parameter…

In this paper, we explore the geometric properties of unbounded extremal domains for the $p$-Laplacian operator in both Euclidean and hyperbolic spaces. Assuming that the nonlinearity grows at least as the nonlinearity of the eigenvalue…

This paper advances the study of multivariate function approximation using neural network operators activated by symmetrized and perturbed hyperbolic tangent functions. We propose new non-linear operators that preserve dynamic symmetries…

We consider second order elliptic operators with real, nonsymmetric coefficient functions which are subject to mixed boundary conditions. The aim of this paper is to provide uniform resolvent estimates for the realizations of these…

In this paper we establish hypercyclicity of continuous linear operators on $H(\mathbb{C})$ that satisfy certain commutation relations.

We prove, by use of inductive techniques, that assorted unbounded composition operators in $L^2$-spaces with matrical symbols are cosubnormal.

It is well-known that, in Linear Dynamics, the most studied class of linear operators is certainly that of weighted shifts, on the separable Banach spaces $c_0$ and $\ell^p$, $1 \leq p< \infty$. Over the last decades, the intensive study of…

In this note basic properties of unbounded weighted conditional expectation operators are investigated. A description of polar decomposition and quasinormality in this context are provided. Also, we study hyperexpan- sive weighted…

We present maximality results in the setting of non necessarily bounded operators. In particular, we discuss and establish results showing when the "inclusion" between operators becomes a full equality.

Given a contraction A on a Hilbert space H, an operator T on H is said to be A-invariant if <Tx,x>=<TAx,Ax> for every x in H such that ||Ax||=||x||. In the special case in which both defect indices of A are equal to 1, we show that every…

We prove weighted mixed $L_{p}(L_{q})$-estimates, with $p,q\in(1,\infty)$, for higher-order elliptic and parabolic equations on the half space $\mathbb{R}^{d+1}_{+}$ and on domains with general boundary conditions which satisfy the…

Assume that $Au=f,\quad (1)$ is a solvable linear equation in a Hilbert space $H$, $A$ is a linear, closed, densely defined, unbounded operator in $H$, which is not boundedly invertible, so problem (1) is ill-posed. It is proved that the…

Given a Hermitian vector bundle over an infinite weighted graph, we define the Laplacian associated to a unitary connection on this bundle and study the essential self-adjointness of a perturbation of this Laplacian by an operator-valued…

We derive rates of convergence for the mixing of operators under infinitely divisible measures in the framework of linear dynamics on Banach spaces. Our approach is based on the characterization of mixing in terms of codifference…

In this paper we describe an iterative operator-splitting method for unbounded operators. We derive error bounds for iterative splitting methods in the presence of unbounded operators and semigroup operators. Here mixed applications of…