Renormalised iterated integrals of symbols with linear constraints

Abstract

Given a holomorphic regularisation procedure (e.g. Riesz or dimensional regularisation) on classical symbols, we define renormalised multiple integrals of radial classical symbols with linear constraints. To do so, we first prove the existence of meromorphic extensions of multiple integrals of holomorphic perturbations ofradial symbols with linear constraints and then implement either generalised evaluators or a Birkhoff factorisation. Renormalised multiple integrals are covariant and factorise over independent sets of constraints.

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• Hopf algebras, from basics to applications to renormalization
• Shuffle relations for regularised integrals of symbols
• The noncommutative residue and canonical trace in the light of Stokes' and continuity properties
• Stokes' formulae on classical symbol valued forms and applications
• Renormalization: general theory
• Discrete sums of classical symbols on Z^d and zeta functions associated with Laplacians on tori