Related papers: A few remarks about linear operators and disconnec…

A way to add an extra dimension is briefly discussed.

Some aspects of analysis on disconnected sets are briefly discussed, more along the lines of regions with infinitely many components than Cantor sets.

Some basic facts about Fredholm indices are briefly reviewed, often used in connection with Toeplitz and pseudodifferential operators, and which may be relevant for operators associated to fractals.

We discuss several open problems on spectrally bounded operators, some new, some old, adding in a few new insights.

We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for…

We study some natural operators acting on configurations of points and lines in the plane and remark that many interesting configurations are fixed points for these operators. We review ancient and recent results on line or point…

This is a brief survey which reviews some traditional themes in harmonic analysis and some more recent areas of activity, connected to "analysis on fractals" in particular.

The problem of equivalency for linear differential operators of the first order is discussed.

The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…

We furnish a simple way of constructing an unbounded closed linear operator in a complex Banach space, whose spectrum is an arbitrary nonempty closed, in particular compact, subset of the complex plane.

The focus here is on connected fractal sets with topological dimension 1 and a lot of topological activity, and their connections with analysis.

We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.

Here we look at some situations that are like the unit circle or the real line in some ways, but which can be more complicated or fractal in other ways.

This expository paper discusses some conjectures related to visibility and blockers for sets of points in the plane.

In connection with the Fuglede conjecture, we study the existence of commuting self-adjoint extensions of the partial differential operators on arbitrary, possibly disconnected domains in $\br^d$, the associated unitary group, the spectral…

Algebraic framework for construction of a commuting set of operators that can be interpreted as integrals of motion of the open spin chain with boundary conditions and nearest neighbour interaction is investigated.

In this note we introduce a new technique to answer an issue posed in [7] concerning geometric properties of the set of non-surjective linear operators. We also extend and improve a related result from the same paper.

Multivalued linear operators, also known as linear relations, are studied on a specific class of weighted, composition transforms on Fock space. Basic properties of this class of linear relations, such as closed graph, boundedness, complex…

The present work considers the properties of classes of generally convex sets in the plane known as $1$-semiconvex and weakly $1$-semiconvex. More specifically, the examples of open and closed weakly $1$-semiconvex but non $1$-semiconvex…

We discuss the concept of invariant subspaces for unbounded linear operators, point out some shortcomings of known definitions, and propose our own.