The completeness of the eigenvectors and associated vectors of a self-adjoint quadratic bundle
β Scribed by M. B. Orazov
- Publisher
- Springer US
- Year
- 1976
- Tongue
- English
- Weight
- 214 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0016-2663
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
If A is a completely continuous self-adjoint operator on a Hilbert space, its eigen= values are the values of the inner product (Ax, x) at stationary points on the unit sphere. Gradient procedures can be used to determine eigenvectors and eigenvalues provided that certain regularity conditions hold
S the unit sphere of H. Assume that Ξ» 0 is an isolated eigenvalue of T of odd multiplicity greater than 1. Given an arbitrary operator B:H β H of class C 1 , we prove that for any Ξ΅ = 0 sufficiently small there exists x Ξ΅ β S and Ξ» Ξ΅ near Ξ» 0 , such that Tx Ξ΅ + Ξ΅B(x Ξ΅ ) = Ξ» Ξ΅ x Ξ΅ . This result was c