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On the asymptotic completeness of the Volterra calculus


The Volterra calculus is a simple and powerful pseudodifferential tool for inverting parabolic equations which has found many applications in geometric analysis. An important property in the theory of pseudodifferential operators is asymptotic completeness, which allows the construction of parametrices modulo smoothing operators. In this paper, we present new and fairly elementary proofs of the asymptotic completeness of the Volterra calculus.

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Correspondence to Raphaël Ponge.

Additional information

The author was partially supported by the European RT NetworkGeometric Analysis HPCRN-CT-1999-00118.

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Ponge, R., Mikayelyan, H. On the asymptotic completeness of the Volterra calculus. J. Anal. Math. 94, 249–263 (2004). https://doi.org/10.1007/BF02789049

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  • Heat Kernel
  • Pseudodifferential Operator
  • Conical Singularity
  • Smoothing Operator
  • Spectral Triple