The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent
Optimization and Control
2009-09-11 v3
Abstract
The paper deals with the genericity of domain-dependent spectral properties of the Laplacian-Dirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically non-resonant. The results are obtained by applying global perturbations of the domains and exploiting analytic perturbation properties. The work is motivated by two applications: an existence result for the problem of maximizing the rate of exponential decay of a damped membrane and an approximate controllability result for the bilinear Schr\"odinger equation.
Keywords
Cite
@article{arxiv.0809.2889,
title = {The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent},
author = {Yannick Privat and Mario Sigalotti},
journal= {arXiv preprint arXiv:0809.2889},
year = {2009}
}