Related papers: Further results on regular Fredholm pairs and chai…
We investigate stability of Fredholm properties on interpolation scales of quasi-Banach spaces. This analysis is motivated by problems arising in PDE's and several applications are presented.
The purpose of this paper is to establish the theory of stochastic pseudo-differential operators and give its applications in stochastic partial differential equations. First, we introduce some concepts on stochastic pseudo-differential…
Two variants of generalizations of Hankel operators to the case of linearly ordered abelian groups are considered, criteria of the boundedness and compactness of these operators are given, among them in terms of functions of bounded mean…
We study the parametrized Hamiltonian action functional for finite-dimensional families of Hamiltonians. We show that the linearized operator for the $L^2$-gradient lines is Fredholm and surjective, for a generic choice of Hamiltonian and…
We first give a condition for a normal operator on a Hilbert space to have no nonzero periodic points, then we give a characterization of normal operators with the whole space as periodic points. We proceed to study the structure of…
In this paper we extend the coupled fixed point theorems for mixed monotone operators $F:X \times X \rightarrow X$ obtained in [T.G. Bhaskar, V. Lakshmikantham, \textit{Fixed point theorems in partially ordered metric spaces and…
As we knew, study the perturbation theory of spectra of operator is a very important project in mathematics physics, in particular, in quantum mechanics. In this paper, we characterize the Fredholm perturbation for the Weyl spectrum,…
We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…
In this note, we frst consider boundedness properties of a family of operators generalizing the Hilbert operator in the upper triangle case. In the diagonal case, we give the exact norm of these operators under some restrictions on the…
Withdrawn due to a likely error with the homeomorphism at line (4). Old abstract: In the monograph 'Limit Operators and their Applications in Operator Theory', the authors define the operator spectrum of a band-dominated operator T and…
We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis of fixed point algorithms. Various properties of conically averaged operators are systematically investigated, in particular, the…
Naively, the analytic index of a family of self-adjoint Fredholm operators ought to be (an equivalence class of) the family of the kernels of these operators. The present paper is devoted to a rigorous version of this idea based on ideas of…
In this paper we characterize EP operators through the existence of different types of factorizations. Our results extend to EP operators existing characterizations for EP matrices and give new characterizations both for EP matrices and EP…
General first- and higher-order intertwining relations between non-stationary one-dimensional Schr\"odinger operators are introduced. For the first-order case it is shown that the intertwining relations imply some hidden symmetry which in…
The purpose of this note is to start the systematic analysis of cofinal types of topological groups.
We study adjointable, bounded operators on the direct sum of two copies of the standard Hilbert C*-module over a unital C*-algebra A that are given by upper triangular 2 by 2 operator matrices. Using the definition of A-Fredholm and…
Motivated by an ongoing project on computer aided derivation of asymptotic models governed by partial differential equations, we introduce a class of term transformations that consists of traversal strategies and insertion of contexts. We…
Denote by $T_n^d(A)$ an upper triangular operator matrix of dimension $n$ whose diagonal entries are given and the others are unknown. In this article we provide necessary and sufficient conditions for various types of Fredholm and Weyl…
The main purpose of this paper is to study the concept of normal function in the context of harmonic mappings from the unit disk $\mathbb{D}$ to the complex plane. In particular, we obtain necessary conditions for that a function $f$ to be…
We revisit a construction principle of Fredholm operators using Hilbert complexes of densely defined, closed linear operators and apply this to particular choices of differential operators. The resulting index is then computed with the help…