Fredholm Property Of Operators Research Articles

Fredholm Property of Operators from 2D String Field Theory

In a recent study of Landau-Ginzburg model of string field theory by Gaiotto, Moore and Witten, there appears a type of perturbed Cauchy-Riemann equation, i.e. the ζ-instanton equation. Solutions of ζ-instanton equation have degenerate asymptotics. This degeneracy is a severe restriction for obtaining the Fredholm property and constructing relevant homology theory. In this article, we study the Fredholm property of a sort of differential operators with degenerate asymptotics. As an application, we verify certain Fredholm property of the linearized operator of ζ-instanton equations.

Two-Dimensional Homogenous Integral Operators and Singular Operators with Measurable Coefficients in Fibers

We study a new class of homogeneous operators in L2( $$ {\mathbb{R}}^2 $$ ) that, after foliation of $$ {\mathbb{R}}^2 $$ into concentric circles, are represented in fibres as singular integral operators with measurable essentially bounded coefficients. We find necessary and sufficient conditions for the invertibility of such operators and construct the operator-valued symbolic calculus for the C∗–algebra generated by such operators and operators of multiplication by multiplicatively weakly oscillating functions. We obtain a criterion for the generalized Fredholm property of operators and find effectively verifiable functional necessary conditions for the classical Fredholm property.

The boundedness and the fredholm property of integral operators with anisotropically homogeneous kernels of compact type and variable coefficients

In the space Lp(ℝn), 1 < p < ∞, we study a new wide class of integral operators with anisotropically homogeneous kernels. We obtain sufficient conditions for the boundedness of operators from this class. We consider the Banach algebra generated by operators with anisotropically homogeneous kernels of compact type and multiplicatively slowly oscillating coefficients. We establish a relationship between this algebra and multidimensional convolution operators, and construct a symbolic calculus for it. We also obtain necessary and sufficient conditions for the Fredholm property of operators from this algebra.

On the spectral properties of differential operators with unbounded operator coefficients determined by a linear relation

Necessary and sufficient conditions for the invertibility and the Fredholm property of operators generated by a family of evolution operators and by the boundary conditions determined by a linear relation are obtained.

Spectral and Fredholm Properties of Operators in Elementary Nest Algebras

Some spectral and Fredholm properties are proved for linear operators which leave invariant certain nests of closed subspaces.

Spectral and Fredholm properties of operators in elementary nest algebras

Some spectral and Fredholm properties are proved for linear operators which leave invariant certain nests of closed subspaces.