Viscosity Limits for Zeroth‐Order Pseudodifferential Operators
نویسندگان
چکیده
Motivated by the work of Colin de Verdière and Saint-Raymond on spectral theory for zeroth-order pseudodifferential operators tori, we consider viscosity limits in which operators, P, are replaced P + iν Δ, ν > 0. By adapting Helffer–Sjöstrand scattering resonances, show that, a complex neighbourhood continuous spectrum, eigenvalues Δ have as goes to In simplified setting this justifies claims made physics literature. © 2021 The Authors. Communications Pure Applied Mathematics published Wiley Periodicals LLC.
منابع مشابه
Pseudodifferential Operators, Corners and Singular Limits
In the first part of my talk I shall describe some of the properties one should expect of a calculus of pseudodifferential operators which corresponds to the microlocalization of a Lie algebra of vector fields. This is not intended to be a formal axiomatic program but it leads one to consider conditions on the Lie algebra for such microlocalization to be possible. The symbolic structure of the ...
متن کاملPseudodifferential 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...
متن کاملIntegral Operators, Pseudodifferential Operators, and Gabor Frames
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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications on Pure and Applied Mathematics
سال: 2022
ISSN: ['1097-0312', '0010-3640']
DOI: https://doi.org/10.1002/cpa.22072