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Weyl composition of symbols in large dimension

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Abstract

This paper is concerned with the Weyl composition of symbols in large dimension. We specify a class of symbols in order to estimate the Weyl symbol of the product of two Weyl h-pseudodifferential operators, with constants independent of the dimension. The proof includes regularized and hybrid compositions, together with a decomposition formula. We also analyze, in this context, the remainder term of the semiclassical expansion of the Weyl composition. The class of symbols contains symbols of Schrödinger semigroups in large dimension, typically for nearest neighbors or mean field interaction potentials. The Weyl composition is applied with Kac operators.

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Authors and Affiliations

  1. LMR EA 4535 et FR CNRS 3399, Université de Reims Champagne-Ardenne, Moulin De La Housse, B. P. 1039, F-51687, Reims, France

    L. Amour & J. Nourrigat

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  1. L. Amour
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  2. J. Nourrigat
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Correspondence to L. Amour.

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Amour, L., Nourrigat, J. Weyl composition of symbols in large dimension. JAMA 130, 375–392 (2016). https://doi.org/10.1007/s11854-016-0041-9

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  • DOI: https://doi.org/10.1007/s11854-016-0041-9

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