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

AN INDEX FORMULA FOR THE EXTENDED HEISENBERG ALGEBRA OF EPSTEIN, MELROSE AND MENDOZA