We consider scattering theory of the Laplace Beltrami operator on differential forms a Riemannian manifold that is Euclidean near infinity. Allowing for compact boundaries low regularity we prove Birman-Krein formula space co-closed forms. In case dimension three this reduces to in Maxwell scattering.

There are two basic angles associated with a pair of linear subspaces: the Diximier angle and Friedrichs angle. These classical notions, which date back to first half 20th century, have been thoroughly studied due their utility in description convergence rates for various projection-based algorithms solving feasibility problems. The Dixmier orthogonal complements is same as original provided ...

We provide a new proof of a theorem of Birman and Solomyak that if A(s) = A0+ sB with B ≥ 0 trace class and dμs(·) = Tr(BEA(s)(·)B), then ∫ 1 0 [dμs(λ)] ds = ξ(λ)dλ where ξ is the Krein spectral shift from A(0) to A(1). Our main point is that this is a simple consequence of the formula: d ds Tr(f(A(s)) = Tr(Bf ′(A(s))). Let A and C = A+B be bounded self-adjoint operators and suppose that B ≥ 0 ...

In this paper we introduce the notion of J-fusion frame for a Krein space K. We prove some basic results regarding J-fusion frame. We also approximate J-fusion frame bounds of a J-fusion frame by the upper and lower bounds of the synthesis operator. Finally we provide a necessary and sufficient condition under which the image of J-fusion frame under a bounded invertible linear map is also a J-f...

An explicit calculation of Casimir effect through an alternative approach of field quantization [1, 2], has been presented in this paper. In this method, the auxiliary negative norm states have been utilized, the modes of which do not interact with the physical states or real physical world. Naturally these modes cannot be affected by the physical boundary conditions. Presence of negative norm ...