Related papers: On the space of Fredholm operators

This note is a description of some of the results obtained by the authors in connection with the problem in the title. These, discussed following a summary of background material concerning wedge differential operators, consist of the…

We consider Toeplitz operators defined on a concave corner-shaped subset of the square lattice. We obtain a necessary and sufficient condition for these operators to be Fredholm. We further construct a Fredholm concave corner Toeplitz…

The paper concerns nonlocal time-periodic boundary value problems for first-order Volterra integro-differential hyperbolic systems with boundary inputs. The systems are subjected to integral boundary conditions. Under natural regularity…

By coupling a Hamiltonian mechanical system with a linear Hamiltonian field theory one obtains an infinite-dimensional Hamiltonian system with regularizing nonlinearity, where the underlying phase space is given by the product of a…

In H\"ormander inner product spaces, we investigate initial-boundary value problems for an arbitrary second order parabolic partial differential equation and the Dirichlet or a general first-order boundary conditions. We prove that the…

We prove novel results on interpolation of Fredholm operators including an abstract factorization theorem. The main result of this paper provides sufficient conditions on the parameters $\theta \in (0,1)$ and $q\in \lbrack 1,\infty ]$ under…

We investigate Lawruk elliptic boundary-value problems for homogeneous differential equations in a two-sided refined Sobolev scale. These problems contain additional unknown functions in the boundary conditions of arbitrary orders. The…

We introduce and study the Rhaly operator on K\"othe spaces, with a primary focus on understanding its well-definedness, continuity, and compactness. We especially examine operators acting on power series spaces of both infinite and finite…

We introduce an extended Sobolev scale on a smooth compact manifold with boundary. The scale is formed by inner-product H\"ormander spaces for which an RO-varying radial function serves as a regularity index. These spaces do not depend on a…

We study boundary conditions for elliptic operators on non-compact manifolds with boundary via uniform K-homology, a version of K-homology sensitive to the large-scale geometry of the manifold. To that end, we develop the theory of relative…

We study the Fredholm solvability for a new class of nonlocal boundary value problems associated with group actions on smooth manifolds. Namely, we consider the case in which the group action is defined on an ambient manifold without…

We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.

In this paper, we introduce statistical bounded set on topological vector space. Also, we consider three classes of bounded operators from topological vector spaces to ordered topological vector spaces. Moreover, we give relations between…

By means of a suitable degree theory, we prove persistence of eigenvalues and eigenvectors for set-valued perturbations of a Fredholm linear operator. As a consequence, we prove existence of a bifurcation point for a non-linear inclusion…

In the present paper we study index theory for families of manifold with corners. In particular the K-theoretical obstruction for an elliptic operator to have a family (Fredholm) index. For codimension 1 corners (families with boundary) it…

Let $A$ be a linear bounded operator in a Hilbert space $H$, $N(A)$ and $R(A)$ its null-space and range, and $A^*$ its adjoint. The operator $A$ is called Fredholm iff $dim N(A)= dim N(A^*):=n<\infty$ and $R(A)$ and $R(A^*)$ are closed…

We develop an elliptic theory based in $L^2$ of boundary value problems for general wedge differential operators of first order under only mild assumptions on the boundary spectrum. In particular, we do not require the indicial roots to be…

In this note known formulas for the product of Toeplitz operators are revisited in the context of their applications to the study of Fredholmness, boundedness of Toeplitz products, and the Berezin-Toeplitz quantization. A few open problems…

We prove a semi-Fredholm theorem for the minimal extension of elliptic operators on manifolds with wedge singularities and give, under suitable assumptions, a full asymptotic expansion of the trace of the resolvent.

We present an improved Fredholm theory of non-elliptic operators for when the corresponding classical dynamical system exhibits normally hyperbolic trapping with smooth backward and forward trapped sets. It takes place on coisotropic…