Related papers: Fredholm-type Operators and Index

Motivated by the dynamics of defects in planar pattern-forming systems, we study Fredholm properties of elliptic operators with singular coefficients in weighted Sobolev spaces. In particular, we consider a family of doubly weighted spaces…

We review an approach to the index theory of operator algebras associated with Lie groups of quantized canonical transformations. Main points are an ellipticity condition ensuring the Fredholm property, the definition of localized algebraic…

Toeplitz operators on spaces $H^p(G)\ (1< p<\infty)$ associated with compact connected Abelian group $G$ with ordered dual are considered and the generalization of the classical Gohberg-Krein theorem on the Fredholm index of such operators…

Criteria for the stability of finite sections of a large class of convolution type operators on $L^p(\mathbb{R})$ are obtained. In this class almost all classical symbols are permitted, namely operators of multiplication with functions in…

In this paper, we established Fredholm theory of the linearized ${{\bar \partial}}$-operator and studied the additivity of its index.

In this paper we show the invariance of the Fredholm index of non-smooth pseudodifferential operators with coefficients in H\"older spaces. By means of this invariance we improve previous spectral invariance results for non-smooth…

We give explicit Fredholm conditions for classes of pseudodifferential operators on suitable singular and non-compact spaces. In particular, we include a "user's guide" to Fredholm conditions on particular classes of manifolds including…

This article provides a version of scale calculus geared towards a notion of (nonlinear) Fredholm maps between certain types of Frechet spaces, retaining as many as possible of the properties Fredholm maps between Banach spaces enjoy, and…

In this article we consider operators of the form $\partial_s\xi+A(s)\xi$ where $s$ lies in an interval $[-T,T]$ and $s\mapsto A(s)$ is continuous. Without boundary conditions these operators are not Fredholm. However, using interpolation…

We introduce and study the Bourgain index of an operator between two Banach spaces. In particular, we study the Bourgain $\ell_p$ and $c_0$ indices of an operator. Several estimates for finite and infinite direct sums are established. We…

We answer the question of when an invariant pseudodifferential operator is Fredholm on a fixed, given isotypical component. More precisely, let $\Gamma$ be a compact group acting on a smooth, compact, manifold $M$ without boundary and let…

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…

Let $G$ be a compact Lie group that acts smoothly on a closed manifold $M$. Using a general Simonenko principle, we derive a novel criterion for the Fredholm property of $G$-pseudodifferential operators acting on Sobolev spaces of sections…

Let $B(\Omega)$ be the Banach space of holomorphic functions on a bounded connected domain $\Omega$ in $\mathbb C^n$, which contains the ring of polynomials on $\Omega $. In this paper, we first establish a criterion for $B(\Omega )$ to be…

We will give a complete description of $\mathcal{I}$, the set of invertible quasicontinuous functions on the unit circle. After doing this, we will then classify the path-connected components of $\mathcal{I}$ and show that $\mathcal{I}$ has…

Let $\Phi$ be a continuous $n\times n$ matrix-valued function on the unit circle $\T$ such that the $(k-1)$th singular value of the Hankel operator with symbol $\Phi$ is greater than the $k$th singular value. In this case, it is well-known…

This paper has aim to characterize Fredholmness and Weylness of upper triangular operator matrices having arbitrary dimension n. We present various characterization results in the setting of infinite dimensional Hilbert spaces, thus…

In this paper a definition is given for an unbounded Toeplitz-like operator with rational symbol which has poles on the unit circle. It is shown that the operator is Fredholm if and only if the symbol has no zeroes on the unit circle, and a…

We study compactness and the Fredholm property for linear operators on coorbit spaces over locally compact abelian phase spaces. In contrast to previous works, we do not impose any countability assumptions on the underlying groups. Our…

Let X be a Banach Space over K=R or C, and let f:=F+C be a weakly coercive operator from X onto X, where F is a C^1-operator, and C a C^1 compact operator. Sufficient conditions are provided to assert that the perturbed operator f is a…