Extending a result of Vassilevich, we obtain the asymptotic expansion for the trace of a spatially regularized heat operator LΘ(f)etΔΘ, where ΔΘ is a generalized Laplacian defined with Moyal products and LΘ(f) is Moyal left multiplication. The Moyal planes corresponding to any skewsymmetric matrix Θ being spectral triples, the spectral action introduced in noncommutative geometry by Chamseddine and Connes is computed. This result generalizes the Connes–Lott action previously computed by Gayral for symplectic Θ.

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