An index formula for the extended Heisenberg algebra of Epstein, Melrose and Mendoza
classification
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math.DG
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formulaoperatorsextendedheisenbergindexalgebracalculuspseudodifferential
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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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