Journal d’Analyse Mathematique

, Volume 94, Issue 1, pp 249–263 | Cite as

On the asymptotic completeness of the Volterra calculus

  • Raphaël Ponge
  • H. Mikayelyan


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.


Heat Kernel Pseudodifferential Operator Conical Singularity Smoothing Operator Spectral Triple 
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© The Hebrew University Magnes Press 2004

Authors and Affiliations

  1. 1.Department of MathematicsOhio State UniversityColumbusUSA
  2. 2.Mathematics InstituteUniversity of LeipzigLeipzigGermany

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