Let X be a locally convex topological vector space, Y a real Banach space, ƒ a mapping (in general, nonlinear) of X into Y. In several recent papers ([5], [ó], [7]), Pohozaev has studied the concept of normal solvability or the Fredholm alternative for mappings ƒ of class C. If Ax=f'x' is the continuous linear mapping of X into Y which is the derivative of ƒ a t the point x of X, A* the adjoint...

This paper studies the Fredholm properties for a class of regular hypoelliptic operators. We establish necessary and sufficient conditions priori estimates differential operators acting in multianisotropic Sobolev spaces R n . criteria index invariance are obtained wide on special scales weighted spaces.

We study weighted composition operators on Banach spaces over unbounded, locally finite metric spaces. characterize the that are bounded, compact, being bounded below, having closed range, invertible, a (surjective) isometry, and Fredholm. Several examples presented illustrating diversity of such operators.

In Dwork’s memoir [3] concerning the rationality of zeta functions, an essential role is played by the p-adic analytic function det(1− tu), where u is a certain infinite matrix. This analytic function is an entire function, exactly as in the classical Fredholm theory. It was natural to pursue this analogy and extend to u the spectral theory of F. Riesz; this is just what Dwork did ([4], §2). In...

Abstract—The scattering of an arbitrary electromagnetic wave by a thin disk located in free space is formulated rigorously in terms of coupled dual integral equations (CDIEs) for the unknown images of the jumps and average values of the normal to the disk scattered-field components. Considered are three cases of the disk: (1) Zero-thickness perfectly electrically conducting (PEC) disk, (2) thin...

one can quantize an invertible symbol σ ∈ C∞(S∗X; hom(π∗E, π∗F )) as an elliptic pseudodifferential operator in the Φ-b or edge calculus, ΨΦ-b(X;E,F ), introduced in [7] or alternately as an elliptic operator in the Φ-c or φ calculus, ΨΦ-c(X;E,F ), introduced in [8]. As on a closed manifold, either of these operators will induce a bounded operator acting between natural L-spaces of sections but...

Let H be a Hilbert space of analytic functions on the unit disk D. For an analytic function ψ on D, we can define the multiplication operator Mψ : f → ψf, f ∈ H. For an analytic selfmapping φ of D, the composition operator Cφ defined on H as Cφf f ◦ φ, f ∈ H. These operators are two classes of important operators in the study of operator theory in function spaces 1–3 . Furthermore, for ψ and φ,...