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Pseudolocality and Microlocality of General Classes of Pseudodifferential Operators
Author(s) -
Staubach Wolfgang
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200103)223:1<121::aid-mana121>3.0.co;2-s
Subject(s) - mathematics , pseudodifferential operators , linear subspace , symbol (formal) , metric (unit) , function (biology) , quantization (signal processing) , pure mathematics , metric space , statistics , computer science , programming language , operations management , evolutionary biology , economics , biology
We study the pseudolocality and microlocality of pseudodifferential operators with general symbols. We treat the problem of pseudo– and microlocality, along finite dimensional linear subspaces, of the Weyl quantization and also generalize some results of Parenti and Rodino to the case of the Weyl–Hörmander calculus of pseudodifferential operators. We do not require that the metric, in the definition of the symbol, is decomposable, σ temperate or satisfy the uncertainty principle neither the weight function of the symbol has to be σ — g temperate. Instead, we assume weaker conditions on the metric and the weight function and the only extra condition we are assuming on the symbol is one of its essential support.