Spectral behaviour of a simple non-self-adjoint operator

Details Spectral behaviour of a simple non-self-adjoint operator Spectral behaviour of a simple non-self-adjoint operator

2001-02-21

arxiv.org/abs/math/0102170v2

Mathematics

Spectral Theory

42 pages, 6 figures

Scientific paper

We investigate the spectrum of a typical non-self-adjoint differential operator $AD=-d^2/dx^2\otimes A$ acting on $\Lp(0,1)\otimes \mathbb{C}^2$, where $A$ is a $2\times 2$ constant matrix. We impose Dirichlet and Neumann boundary conditions in the first and second coordinate respectively at both ends of $[0,1]\subset\mathbb{R}$. For $A\in \mathbb{R}^{2\times 2}$ we explore in detail the connection between the entries of $A$ and the spectrum of $AD$, we find necessary conditions to ensure similarity to a self-adjoint operator and give numerical evidence that suggests a non-trivial spectral evolution.

Affiliated with

Also associated with

No associations

Rating

Spectral behaviour of a simple non-self-adjoint operator does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Spectral behaviour of a simple non-self-adjoint operator, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spectral behaviour of a simple non-self-adjoint operator will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-520369