Projective structures of elliptic differential operators

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

The Index of Projective Families of Elliptic Operators

An index theory for projective families of elliptic pseudodifferential operators is developed. The topological and the analytic index of such a family both take values in twisted K-theory of the parametrizing space. The main result is the equality of these two notions of index when the twisting class is in the torsion subgroup tor(H3(X;Z)) and the Chern character of the index class is then comp...

Equivariant and Fractional Index of Projective Elliptic Operators

In this note the fractional analytic index, for a projective elliptic operator associated to an Azumaya bundle, of [5] is related to the equivariant index of [1, 6] for an associated transversally elliptic operator.

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...

On Elliptic Differential Operators with Shifts

The motivating point of our research was differential operators on the noncommutative torus studied by Connes [1, 2], who in particular obtained an index formula for such operators. These operators include shifts (more precisely, in this case, irrational rotations); hence our interest in general differential equations with shifts naturally arose. Let M be a smooth closed manifold. We consider o...