An index formula for the extended Heisenberg algebra of Epstein, Melrose and Mendoza

Details An index formula for the extended Heisenberg algebra of Epstein, Melrose and Mendoza An index formula for the extended Heisenberg algebra of Epstein, Melrose and Mendoza

2010-07-20

arxiv.org/abs/1007.3532v2

Mathematics

Functional Analysis

Scientific paper

The extended Heisenberg algebra for a contact manifold has a symbolic calculus that accommodates both Heisenberg pseudodifferential operators as well as classical pseudodifferential operators. We derive here a formula for the index of Fredholm operators in this extended calculus. This formula incorporates in a single expression the Atiyah-Singer formula for elliptic operators, as well as Boutet de Monvel's Toeplitz index formula.

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