The Wodzicki residue for pseudo-differential operators on compact Lie groups

2022/01/28 by Duván Cardona, Cardona, Duván
Mathematics · #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Representation Theory (math.RT) #Spectral Theory (math.SP) #math.CV #math.DG #math.FA #math.RT #math.SP

paper · pdf · doi:10.48550/arxiv.2201.12336

12 Pages. arXiv admin note: text overlap with arXiv:2110.00838

arxiv created 2022/01/31 · arxiv updated 2022/02/02

Abstract

Let G be an arbitrary compact Lie group. In this work we apply the method of the analytic continuation of traces in order to compute the Wodzicki residue for a classical pseudo-differential operator on G in terms of its matrix-valued symbol (which is globally defined on the non-commutative phase space G× \widehatG, with \widehatG being the unitary dual of G). Our main theorem is complementary to the results in [2], where we remove the ellipticity hypothesis when the operators belong to the Hörmander classes on G defined by local coordinate systems.

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