Abstract
Let F be a polarisation, in the sense of Kostant, of a 2 n-dimensional symplectic manifold M, and let L be a complex line bundle with flat connection along F. We prove, under suitable conditions, that the r-dim. cohomology of C ∞ L-valued half forms normal to F with forms on F as coefficients, has as dual space the ( n− r)-dim. cohomology of compactly supported distributional L ∗-valued half forms normal to F with forms on F as coefficients. We deduce that the spectrum of an F-preserving function ϕ is the same when quantised on the highest C ∞ cohomology as when quantised on the compactly supported distributional sections.
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