Elliptic operators in odd subspaces

Details Elliptic operators in odd subspaces Elliptic operators in odd subspaces

1999-07-07

arxiv.org/abs/math/9907039v1

Matem. Sbornik 191, N.8, 89-112, 2000. English transl.: Sb.:Mathematics, 191, N. 8 (2000), 1191-1213

Mathematics

Differential Geometry

27 pages

Scientific paper

An elliptic theory is constructed for operators acting in subspaces defined via odd pseudodifferential projections. Subspaces of this type arise as Calderon subspaces for first order elliptic differential operators on manifolds with boundary, or as spectral subspaces for self-adjoint elliptic differential operators of odd order. Index formulas are obtained for operators in odd subspaces on closed manifolds and for general boundary value problems. We prove that the eta-invariant of operators of odd order on even-dimesional manifolds is a dyadic rational number.

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