Related papers: Inversion of an analytic operator function through…

We show that on the real $2$-dimensional Banach space $\ell_1^2$ there is an analytic function $f:B_{\ell_1^2}\rightarrow \mathbb{R}$ such that its power series at origin has radius of uniform convergence one, but for some $a\in…

This paper is a continuation of the paper (A.G.Ramm, Amer. Math. Monthly, 108, N 9, (2001), 855-860), where bounded Fredholm operators are studied. The theory of bounded linear Fredholm-type operators is presented in many texts. This paper…

This paper presents a multivariate generalization of Flajolet and Odlyzko's transfer theorem. Similarly to the univariate version, the theorem assumes $\Delta$-analyticity (defined coordinate-wise) of a function $A(z_1,\ldots,z_d)$ at a…

We provide a characterization of the commutant of analytic Toeplitz operators $T_B$ induced by finite Blachke products $B$ acting on weighted Bergman spaces which, as a particular instance, yields the case $B(z)=z^n$ on the Bergman space…

Let $\Lambda$ be an open set in Banach space $E$, $M(x)$ for $x\in \Lambda $ be a subspace in $E$, and $x_0$ be a point in $\Lambda $. We consider the family $\mathcal{F}=\{M(x):\forall x\in\Lambda\}$, but the dimension of $M(x)$ can be…

In this paper we shall focus on one-dimensional strictly local operators, the notion of which naturally arises in the context of discrete-time quantum walks on the one-dimensional integer lattice. In particular, we give an elementary…

This is (raw) lecture notes of the course read on 6th European intensive course on Complex Analysis (Coimbra, Portugal) in 2000. Our purpose is to describe a general framework for generalizations of the complex analysis. As a consequence a…

We define classes of pseudodifferential operators on $G$-bundles with compact base and give a generalized $L^2$ Fredholm theory for invariant operators in these classes in terms of von Neumann's $G$-dimension. We combine this formalism with…

Starting from the definition of A-Fredholm and semi-A-Fredholm operator on the standard module over a unital C*- algebra A, introduced in [8] and [4], we construct various generalizations of these operators and obtain several results as an…

We use properties of the sequences of zeros of certain spaces of analytic functions in the unit disc $\mathbb D$ to study the question of characterizing the weighted superposition operators which map one of these spaces into another. We…

The condition onto pair ($F,G$) of function Banach spaces under which there exists a integral operator $T:F\to G$ with analytic kernel such that the inverse mapping $T^{-1}:$im$T\to F$ does not belong to arbitrary a priori given Borel (or…

We give conditions for local diagonalization of an analytic operator family to a diagonal operator polynomial. The families are acting between real or complex Banach spaces. The basic assumption is given by stabilization of the Jordan…

This paper is devoted to studying the extrapolation theory of Rubio de Francia on general function spaces. We present endpoint extrapolation results including $A_1$, $A_p$, and $A_\infty$ extrapolation in the context of Banach function…

Given a Hodge manifold, it is introduced a self-adjoint operator on the space of endomorphisms of the global holomorphic sections of the polarization line bundle. Such operator is shown to approximate the Laplace operator on functions when…

Emil Artin defined a zeta function for algebraic curves over finite fields and made a conjecture about them analogous to the famous Riemann hypothesis. This and other conjectures about these zeta functions would come to be called the Weil…

We establish several fundamental properties of one-sided (generalized) Drazin inverses in Banach algebras, including intertwining properties and reverse order laws. In particular, we introduce the concepts of one-sided strongly…

We study the convergence of these operators in a weighted space of functions on a positive semi-axis and estimate the approximation by using a new type of weighted modulus of continuity and error estimation.

A non-local modified gravity model with an analytic function of the d'Alembert operator that has been proposed as a possible way of resolving the singularities problems in cosmology is considered. We show that the anzats that is usually…

We prove an extrapolation of compactness theorem for operators on Banach function spaces satisfying certain convexity and concavity conditions. In particular, we show that the boundedness of an operator $T$ in the weighted Lebesgue scale…

We introduce and study some operational quantities which characterize the disjointly non-singular operators from a Banach lattice $E$ to a Banach space $Y$ when $E$ is order continuous, and some other quantities which characterize the…