Desuspension of splitting elliptic symbols. I (Q1080249)

Let A be an elliptic first-order differential operator on the terms \(Y\times S^ 1\), Y a smooth closed manifold. It is supposed that A splits into \(\partial /\partial t+B_ t\), where \(\{B_ t\}\) is a family of self-adjoint elliptic operators satisfying a suitable periodicity condition. The paper provides an algorithm for the conversion of the index of A into the index of a canonically associated elliptic pseudo- differential operator Q on Y. Applications are given for the calculation of the index of the general linear conjugation problem.