Spectral decomposition of a perturbed differential operator
โ Scribed by E. V. Cheremnykh
- Book ID
- 112471890
- Publisher
- Springer
- Year
- 1989
- Tongue
- English
- Weight
- 340 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0041-5995
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The authors study symmetric operator matrices A B = ( B ' C ) in the product of Hilbert spaces H = Hi xH2, where the entries are not necessarily bounded operators. Under suitable assumptions the closure Lo exists and is a selfadjoint operator in H. With Lo, the closure of the transfer function M(X)
It is shown that the operator p2 \_ q2 has a continuous spectrum extending from --00 to + oo. The expansion of an arbitrary function with respect to the eigenfunctions is given. The action of the operators q and p on the eigenfunctions can be written explicitly by means of symbolic formulae. Finally