On summability of distributions and spectral geometry

Abstract

Modulo the moment asymptotic expansion, the Cesaro and parametric behaviours of distributions at infinity are equivalent. On the strength of this result, we construct the asymptotic analysis for spectral densities, arising from elliptic pseudodifferential operators. We show how Cesaro developments lead to efficient calculations of the expansion coefficients of counting number functionals and Green functions. The bosonic action functional proposed by Chamseddine and Connes can more generally be validated as a Cesaro asymptotic development.

34 pages, Plain TeX

References in corpus (4)

• An Introduction to Noncommutative Spaces and their Geometry
• Zeta-function regularization, the multiplicative anomaly and the Wodzicki residue
• Measures from Dixmier Traces and Zeta Functions
• On Connes' new principle of general relativity. Can spinors hear the forces of spacetime?

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• Forces from Connes' geometry
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• Noncommutative Yang-Mills and Noncommutative Relativity: A Bridge Over Trouble Water
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• The interface of noncommutative geometry and physics
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