A Weyl pseudodifferential calculus associated with exponential weights on ℝ^d

2020/01/14 by Sean Harris, Harris, Sean
Mathematics · #47A60 (Primary) 35S05 #47F05 (Secondary) #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2001.04572

openalex publication_date 2020/01/14 · openalex created_date 2020/01/23 · openalex updated_date 2026/07/28

Abstract

We construct a Weyl pseudodifferential calculus tailored to studying boundedness of operators on weighted L^p spaces over ℝ^d with weights of the form exp(-ϕ(x)), for ϕ a C² function, a setting in which the operator associated to the weighted Dirichlet form typically has only holomorphic functional calculus. A symbol class giving rise to bounded operators on L^p is determined, and its properties analysed. This theory is used to calculate an upper bounded on the H^∞ angle of relevant operators, and deduces known optimal results in some cases. Finally, the symbol class is enriched and studied under an algebraic viewpoint.

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