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Renormalised Multiple Integrals of Symbols with Linear Constraints

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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 of radial 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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  1. Laboratoire de Mathématiques, Complexe des Cézeaux, Université Blaise Pascal, 63 177, Aubière Cedex, France

    Sylvie Paycha

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  1. Sylvie Paycha
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Correspondence to Sylvie Paycha.

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Communicated by A. Connes

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Paycha, S. Renormalised Multiple Integrals of Symbols with Linear Constraints. Commun. Math. Phys. 286, 495–540 (2009). https://doi.org/10.1007/s00220-008-0675-2

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  • DOI: https://doi.org/10.1007/s00220-008-0675-2

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