On the asymptotic completeness of the Volterra calculus

Raphaël Ponge; H. Mikayelyan

doi:10.1007/BF02789049

On the asymptotic completeness of the Volterra calculus

Raphaël Ponge, H. Mikayelyan

Research output: Journal Publication › Review article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	249-263
Number of pages	15
Journal	Journal d'Analyse Mathematique
Volume	94
DOIs	https://doi.org/10.1007/BF02789049
Publication status	Published - 2004
Externally published	Yes

ASJC Scopus subject areas

Analysis
General Mathematics

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10.1007/BF02789049

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title = "On the asymptotic completeness of the Volterra calculus",

abstract = "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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AU - Ponge, Raphaël

AU - Mikayelyan, H.

PY - 2004

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N2 - 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.

AB - 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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U2 - 10.1007/BF02789049

DO - 10.1007/BF02789049

M3 - Review article

AN - SCOPUS:14644413504

SN - 0021-7670

VL - 94

SP - 249

EP - 263

JO - Journal d'Analyse Mathematique

JF - Journal d'Analyse Mathematique

ER -

On the asymptotic completeness of the Volterra calculus

Abstract

ASJC Scopus subject areas

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