Functional calculi for pseudodifferential operators, III
نویسندگان
چکیده
منابع مشابه
Pseudodifferential Operators
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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This chapter illustrates the use of Gabor frame analysis to derive results on the spectral properties of integral and pseudodifferential operators. In particular, we obtain a sufficient condition on the kernel of an integral operator or the symbol of a pseudodifferential operator which implies that the operator is trace-class. This result significantly improves a sufficient condition due to Dau...
متن کاملSymplectic inverse spectral theory for pseudodifferential operators
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.
متن کاملDispersive Estimates for Principally Normal Pseudodifferential Operators
The aim of these notes is to describe some recent results concerning dispersive estimates for principally normal pseudodifferential operators. The main motivation for this comes from unique continuation problems. Such estimates can be used to prove L Carleman inequalities, which in turn yield unique continuation results for various partial differential operators with rough potentials.
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This is a survey on trace constructions on various operator algebras with an emphasis on regularized traces on algebras of pseudodifferential operators. For motivation our point of departure is the classical Hilbert space trace which is the unique semifinite normal trace on the algebra of bounded operators on a separable Hilbert space. Dropping the normality assumption leads to the celebrated D...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1989
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-95-2-155-173