The Invertible Double of Elliptic Operators

The invertible double of elliptic operators

We construct a canonical invertible double for general first order elliptic differential operators over smooth compact manifolds with boundary and derive a natural formula for the Calderón projector which yields a generalization of the famous Cobordism Theorem. Assuming symmetric principal symbol of the tangential operator and unique continuation property (UCP) from the boundary, we obtain the ...

Affine Mappings of Invertible Operators

The infinite-dimensional analogues of the classical general linear group appear as groups of invertible elements of Banach algebras. Mappings of these groups onto themselves that extend to affine mappings of the ambient Banach algebra are shown to be linear exactly when the Banach algebra is semi-simple. The form of such linear mappings is studied when the Banach algebra is a C*-algebra.

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...

Transversally Elliptic Operators

In this paper we investigate the index theory of transversally elliptic pseudo-differential operators in the framework of noncommutative geometry. We give examples of spectral triples in the sense of Alain Connes and Henri Moscovici in [12] that are transversally elliptic but nonelliptic. We prove that these spectral triples satisfy the conditions which ensure the Connes-Moscovici local index f...