On summability of distributions and spectral geometry
Modulo the moment asymptotic expansion, the Cesàro 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 Cesàro 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 Cesàro asymptotic development.
Publication Source (Journal or Book title)
Communications in Mathematical Physics
Estrada, R., Gracia-Bondía, J., & Várilly, J. (1998). On summability of distributions and spectral geometry. Communications in Mathematical Physics, 191 (1), 219-248. https://doi.org/10.1007/s002200050266