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Norm closure of classical pseudodifferential operators does not contain Hörmander's class

2003/12/12 by Severino T. Melo, Melo, Severino T.
Computer Science · Mathematics · Physics and Astronomy · #35S05 #47G30 #58J40 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA) #Topological and Geometric Data Analysis #math.AP #math.OA #msc:35S05 #msc:47G30 #msc:58J40

paper · pdf · doi:10.48550/arxiv.math/0312261

arxiv created 2003/12/12 · openalex publication_date 2003/12/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The L2-norm closure of the algebra of all zero-order classical (or polyhomogeneous) pseudodifferential operators on a closed manifold X is proven not to contain Hörmander's class Ψ0(X). A set of generators (for that closed algebra) smaller than all zero-order classical pseudos is also described.

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