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Positivity results for Weyl’s pseudo-differential calculus on the Wiener space

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Abstract

This paper deals with positivity properties for a pseudo-differential calculus, generalizing Weyl’s classical quantization, and set on an infinite dimensional configuration space, the Wiener space. In this frame, we show that a positive symbol does not, in general, give a positive operator. In order to measure the nonpositivity, we establish a Gårding’s inequality, which holds for the symbol classes at hand. Nevertheless, for symbols with radial aspects, additional assumptions ensure the positivity of the associated operator.

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  1. Laboratoire de Mathématiques de Reims - UMR CNRS 9008, Université de Reims Champagne-Ardenne, Moulin de la Housse, BP 1039, 51687 Cedex 2, Reims, France

    Lisette Jager

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L Jager wrote and reviewed the manuscript.

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Correspondence to Lisette Jager.

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Jager, L. Positivity results for Weyl’s pseudo-differential calculus on the Wiener space. J. Pseudo-Differ. Oper. Appl. 14, 34 (2023). https://doi.org/10.1007/s11868-023-00526-6

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  • DOI: https://doi.org/10.1007/s11868-023-00526-6

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