Related papers: On the space of Fredholm operators
We present two applications of explicit formulas, due to Cuntz and Krieger, for computations in K-homology of graph C*-algebras. We prove that every K-homology class for such an algebra is represented by a Fredholm module having finite-rank…
We prove the Fredholm alternative for a class of two-dimensional first-order hyperbolic systems with periodic-Dirichlet boundary conditions. Our approach is based on a regularization via a right parametrix.
We survey recent progress in a program aimed at proving general Fatou-type results and establishing the well-posedness of a variety of boundary value problems in the upper half-space ${\mathbb{R}}^n_{+}$ for second-order, homogeneous,…
We introduce Besov and Triebel--Lizorkin spaces on a manifold with boundary adapted to H\"ormander vector fields, near a so-called non-characteristic point of the boundary. We prove sharp results in these spaces for the corresponding…
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…
We describe a very general (nonlinear) Fredholm theory for a new class of ambient spaces, called polyfolds. This theory is applicable to Gromov-Witten and Floer Theory as well as Symplectic Field Theory. It should also be applicable to a…
Several mathematicians, including myself, have studied some unifications in general topological spaces as well as in fuzzy topological spaces. For instance in our earlier works, using operations on topological spaces, we have tried to unify…
Semigroups generated by topological operations such as closure, interior or boundary are considered. It is noted that some of these semigroups are in general finite and noncommutative. The problem is formulated whether they are always…
This paper concerns hyperbolic systems of two linear first-order PDEs in one space dimension with periodicity conditions in time and reflection boundary conditions in space. The coefficients of the PDEs are supposed to be time independent,…
The topology of spaces of Hermitian operators in $C^n$ with non-simple spectra was studied by V.Arnold in a relation with the theory of adiabatic connections and the quantum Hall effect. The natural filtration of these spaces by the sets of…
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…
We establish local interval bifurcation theorem and global interval bifurcation theorem for Fredholm operator with index $0$ via $0$-group. As one of applications, we investigate the existence of a family of nontrivial domains…
We study and compare the gap and the Riesz topologies of the space of all unbounded regular operators on Hilbert C*-modules. We show that the space of all bounded adjointable operators on Hilbert C*-modules is an open dense subset of the…
We discuss several natural metrics on spaces of unbounded self--adjoint operators and their relations, among them the Riesz and the graph metric. We show that the topologies of the spaces of Fredholm operators resp. invertible operators…
For systems of ordinary differential equations on a compact interval, we study the character of solvability of the most general linear boundary-value problems in Sobolev spaces. We find the indices of these problems and obtain a criterion…
This is a companion to recent papers of the authors; here we construct the `noncommutative Shilov boundary' of a (possibly nonunital) selfadjoint ordered space of Hilbert space operators. The morphisms in the universal property of the…
We present the set of axioms for topological space with the operation of boundary as primitive notion.
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…
On filtered manifolds one can define a different notion of order for the differential operators. In this paper, we use generalized fixed point algebras to construct a pseudodifferential extension that reflects this behaviour. In the…
We study a natural family of non-local elliptic boundary problems on a compact oriented surface $\Sigma$ parametrized by the moduli space $\mathcal{M}_\Sigma$ of flat $G$-connections with framing along $\partial \Sigma$. This family…