Foundation of symbol theory for analytic pseudodifferential operators, I
نویسندگان
چکیده
منابع مشابه
Pseudodifferential operators and weighted normed symbol spaces
In this work we study some general classes of pseudodifferential operators where the classes of symbols are defined in terms of phase space estimates. Résumé On étudie des classes générales d’opérateurs pseudodifférentiels dont les classes de symboles sont définis en termes d’éstimations dans l’espace de phase.
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We prove, under some generic assumptions, that the semiclassical spectrum modulo O(~) of a one dimensional pseudodifferential operator completely determines the symplectic geometry of the underlying classical system. In particular, the spectrum determines the hamiltonian dynamics of the principal symbol.
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The study of pseudodifferential operators emerged in the 1960’s, having its origins in the study of singular integro-differential operators. In fact, Friedrichs and Lax coined the term “pseudodifferential operator” in their 1965 paper entitled “Boundary Value Problems for First Order Operators”. Since that time, pseudodifferential operators have proved useful in many arenas of modern analysis a...
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Motivated by the problem of channel estimation in wireless communications, we derive a reconstruction formula for pseudodifferential operators with a bandlimited symbol. This reconstruction formula uses the diagonal entries of the matrix of the pseudodifferential operator with respect to a Gabor system. In addition, we prove several other uniqueness theorems that shed light on the relation betw...
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 2017
ISSN: 0025-5645
DOI: 10.2969/jmsj/06941715