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Results tagged with eigenvalues
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user 13093
eigenvalues of matrices or operators
1
vote
0
answers
73
views
Eigenvalue overdetermined problem
The proof of the above fact relies on $u>0$, so it cannot be adapted for higher eigenvalues. …
- 2,222
4
votes
0
answers
50
views
Computing quantities related to the Dirichlet Laplace eigenfunctions
Consider the Dirichlet-Laplace eigenvalue problem
$$\left\{ \begin{array}{rccl}
-\Delta u & = & \lambda u & \text{ in }\Omega\\
u& = & 0 & \text{ on }\Omega
\end{array}\right.$$
Suppose $\lambda$ is …
- 2,222
0
votes
1
answer
703
views
Stability of eigenvectors for diagonal perturbations
In a previous question I asked about the stability of eigenvalues with respect to diagonal perturbations. Following results from the book Matrix Analysis (by Roger A. Horn & Charles R. …
- 2,222
12
votes
0
answers
209
views
Classes for which the Spectrum determines a Convex Shape
Given a planar domain $\Omega \subset \Bbb{R}^2$ bounded and open we can associate to it the spectrum of the Laplace operator with Dirichlet boundary condition. It is known that there are planar domai …
- 2,222
7
votes
1
answer
6k
views
Eigenvectors as continuous functions of matrix - diagonal perturbations
The general question has been treated here, and the response was negative. My question is about more particular perturbations. The counterexamples given in the previous question have variations not on …
- 2,222