Riesz basis for strongly continuous groups


Zwart, H.J. (2010) Riesz basis for strongly continuous groups. Journal of differential equations, 249 (10). pp. 2397-2408. ISSN 0022-0396

[img] PDF
Restricted to UT campus only
: Request a copy
Abstract:Given a Hilbert space and the generator of a strongly continuous group on this Hilbert space. If the eigenvalues of the generator have a uniform gap, and if the span of the corresponding eigenvectors is dense, then these eigenvectors form a Riesz basis (or unconditional basis) of the Hilbert space. Furthermore, we show that none of the conditions can be weakened. However, if the eigenvalues (counted with multiplicity) can be grouped into subsets of at most K elements, and the distance between the groups is (uniformly) bounded away from zero, then the spectral projections associated to the groups form a Riesz family. This implies that if in every range of the spectral projection we construct an orthonormal basis, then the union of these bases is a Riesz basis in the Hilbert space
Item Type:Article
Copyright:© 2010 Elsevier
Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:
Link to this item:http://purl.utwente.nl/publications/73945
Official URL:https://doi.org/10.1016/j.jde.2010.07.020
Export this item as:BibTeX
HTML Citation
Reference Manager


Repository Staff Only: item control page

Metis ID: 271162