Related papers: Inversion of an analytic operator function through…
We consider special classes of linear bounded operators in Banach spaces and suggest certain operator variant of symbolic calculus. It permits to formulate an index theorem and to describe Fredholm properties of elliptic pseudo-differential…
A bounded operator $T$ on a separable, complex Hilbert space is said to be odd symmetric if $I^*T^tI=T$ where $I$ is a real unitary satisfying $I^2=-1$ and $T^t$ denotes the transpose of $T$. It is proved that such an operator can always be…
This paper investigates the transformation of determinants of pairs of Fredholm operators with trace class commutators. We study the extent to which the functional calculus commutes, modulo operator ideals, with projections in a finitely…
We extend the concept of average expansivity for operators on Banach spaces to operators on arbitrary locally convex spaces. We obtain complete characterizations of the average expansive weighted shifts on Fr\'echet sequence spaces.…
Using the general formalism of [12], a study of index theory for non-Fredholm operators was initiated in [9]. Natural examples arise from $(1+1)$-dimensional differential operators using the model operator $D_A$ in $L^2(\mathbb{R}^2; dt…
This paper concerns the analysis of an unbounded Toeplitz-like operator generated by a rational matrix function having poles on the unit circle T. It extends the analysis of such operators generated by scalar rational functions with poles…
Given a Banach lattice $L,$ the space of lattice Lipschitz operators on $L$ has been introduced as a natural Lipschitz generalization of the linear notions of diagonal operator and multiplication operator on Banach function lattices. It is…
Let $V$ be a {\em periodic} potential on $\RR^3$ that is smooth everywhere except at a discrete set $\maS$ of points, where it has singularities of the form $Z/\rho^2$, with $\rho(x) = |x - p|$ for $x$ close to $p$ and $Z$ is continuous,…
In this article, we present a solution to the problem: "Which type of linear operators can be realized by the Dirichlet-to-Neumann operator associated with the operator $-\Delta-a(z)\frac{\partial^{2}}{\partial z^2}$ on an extension…
Let $\mathcal{B}(\mathcal{H})$ denote the Banach algebra of all bounded linear operators acting on complex Hilbert spaces $\mathcal{H}$. In this paper, we first establish several sharply refined versions of Bohr's inequality analogues with…
In this paper we define a regularized version of the analytic torsion for quotients of a symmetric space of non-positive curvature by arithmetic lattices. The definition is based on the study of the renormalized trace of the corresponding…
Since the Hadamard Theorem, several metric and topological conditions have emerged in the literature to date, yielding global inversion and implicit theorems for functions in different settings. Relevant examples are the mappings between…
We introduce and study some (infinite order) discrete derivative operators called Bernoulli operators. They are associated to a class of power series (tame power series), which include power series that converge in the unit disk, have at…
We consider the task of computing an approximate minimizer of the sum of a smooth and non-smooth convex functional, respectively, in Banach space. Motivated by the classical forward-backward splitting method for the subgradients in Hilbert…
In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…
The asymptotic properties of integral operators with the generalized sine kernel acting on the real axis are studied. The formulas for the resolvent and the Fredholm determinant are obtained in the large x limit. Some applications of the…
The functor of second quantization as well as quadratic creation and annihilation operators on the bosonic Fock space are defined through possibly infinite series. The domain of convergence is investigated by precise number operator…
Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fr\'echet space of all Dirichlet series that are uniformly convergent in all half-planes $\{s \in \mathbb{C}…
In an earlier paper, we showed that the moduli space of deformations of a smooth, compact, orientable special Lagrangian submanifold L in a symplectic manifold X with a non-integrable almost complex structure is a smooth manifold of…
Given parameters $x \notin \mathbb{R}^- \cup \{1\}$ and $\nu$, $\mathrm{Re}(\nu) < 0$, and the space $\mathscr{H}_0$ of entire functions in $\mathbb{C}$ vanishing at $0$, we consider the family of operators $\mathfrak{L} = c_0 \cdot \delta…