Elliptic operators in odd subspaces
Sbornik. Mathematics, Tome 191 (2000) no. 8, pp. 1191-1213

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An elliptic theory is constructed for operators acting in subspaces defined by means of odd pseudodifferential projections. Index formulae for operators on compact manifolds without boundary and for general boundary-value problems are obtained. A connection with Gilkey's theory of $\eta$-invariants is established.
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     title = {Elliptic operators in odd subspaces},
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A. Yu. Savin; B. Yu. Sternin. Elliptic operators in odd subspaces. Sbornik. Mathematics, Tome 191 (2000) no. 8, pp. 1191-1213. http://geodesic.mathdoc.fr/item/SM_2000_191_8_a3/