2022/05/09 by Lisette Jager, Jager, Lisette
Mathematics · #35S99 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2205.04091
openalex publication_date 2022/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper deals with positivity properties for a pseudodifferential calculus, generalizing Weyl's classical quantization, and set on an infinite dimensional phase 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.