Pseudospectra in a non-Archimedean Banach space and essential pseudospectra in Eω

About Deenitions of Pseudospectra of Closed Operators in Banach Spaces

Our goal, in this paper, is to study some equivalent deenitions of the pseudospectra of a closed linear operator. We start from two deenitions, one with strict inequality and the other with non-strict inequality. The rst deenition makes the pseudospectrum open and the second makes it closed. We will show the subtle diierence between these seemingly almost identical deenitions and the relations ...

Non-Self-Adjoint Operators and Pseudospectra

The theory of pseudospectra has grown rapidly since its emergence from within numerical analysis around 1990. We describe some of its applications to the stability theory of differential operators, to WKB analysis and even to orthogonal polynomials. Although currently more a way of looking at non-self-adjoint operators than a list of theorems, its future seems to be assured by the growing numbe...

Pseudospectra in Automorphic Scattering

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...

Characteristic polynomials and pseudospectra

In this paper, we study the ε-lemniscate of the characteristic polynomial in relation to the pseudospectrum of the associated matrix. It is natural to investigate this question because these two sets can be seen as generalizations of eigenvalues. The question of numerical determination of the ε-lemniscate raises the problem of computing the characteristic polynomial p. We can express the coeffi...