Semi-classical Analysis and Pseudospectra
نویسنده
چکیده
We prove an approximate spectral theorem for non-self-adjoint operators and investigate its applications to second order differential operators in the semi-classical limit. This leads to the construction of a twisted FBI transform. We also investigate the connections between pseudospectra and boundary conditions in the semi-classical limit. AMS subject classification numbers: 81Q20, 47Axx, 34Lxx.
منابع مشابه
Semi-classical Analysis and Pseudospectra Sap2.tex
We prove an approximate spectral theorem for non-self-adjoint operators and investigate its applications to second order differential operators in the semi-classical limit. This leads to the construction of a twisted FBI transform. We also investigate the connections between pseudospectra and boundary conditions in the semi-classical limit.
متن کاملStructured Pseudospectra and Random Eigenvalues Problems in Vibrating Systems
This paper introduces the concept of pseudospectra as a generalized tool for uncertainty quantification and propagation in structural dynamics. Different types of pseudospectra of matrices and matrix polynomials are explained. Particular emphasis is given to structured pseudospectra for matrix polynomials, which offer a deterministic way of dealing with uncertainties for structural dynamic syst...
متن کاملNon-selfadjoint Harmonic Oscillator, Compact Semigroups and Pseudospectra
We provide new information concerning the pseudospectra of the complex harmonic oscillator. Our analysis illustrates two different techniques for getting resolvent norm estimates. The first uses the JWKB method and extends for this particular potential some results obtained recently by E.B. Davies. The second relies on the fact that the bounded holomorphic semigroup generated by the complex har...
متن کاملCompact Semigroups and Pseudospectra
We provide new information concerning the pseudospectra of the complex harmonic oscillator. Our analysis illustrates two different techniques for getting resolvent norm estimates. The first uses the JWKB method and extends for this particular potential some results obtained recently by E.B. Davies. The second relies on the fact that the bounded holomorphic semigroup generated by the complex har...
متن کاملA Fast Algorithm for Computing Pseudospectra of Companion Matrices
The concept of pseudospectra was introduced by Trefethen during the 1990s and became a popular tool to explain the behavior of non-normal matrices. It is well known that the zeros of a polynomial are equal to the eigenvalues of the associated companion matrix. It is feasible to do the sensitivity analysis of the zeros of polynomials by the tool of pseudospectra of companion matrices. Thus, the ...
متن کامل