Rank One Perturbations at Infinite Coupling
β Scribed by F. Gesztesy; B. Simon
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 229 KB
- Volume
- 128
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
of a semibounded selfadjoint operator A are studied with the help of distribution theory. It is shown that such perturbations can be defined for finite values of : even if the element . does not belong to H &1 (A). Approximations of the rank one perturbations are constructed in the strong operator t
Let N 1 denote the class of generalized Nevanlinna functions with one negative square and let N 1, 0 be the subclass of functions Q(z) Β₯ N 1 with the additional properties lim y Q . Q(iy)/y=0 and lim sup y Q . y |Im Q(iy)| < .. These classes form an analytic framework for studying (generalized) rank
## Abstract Let __A__ be a selfβadjoint operator and __Ο__ its cyclic vector. In this work we study spectral properties of rank one perturbations of __A__ __A~ΞΈ~__ = __A__ + __ΞΈ__ γ__Ο__ , Β·γ__Ο__ in relation to their dependence on the real parameter __ΞΈ__ . We find bounds on averages of spectr
Replacing invertibility with quasi-invertibility in Bass' first stable range condition we discover a new class of rings, the QB-rings. These constitute a considerable Ε½ . enlargement of the class of rings with stable rank one B-rings and include Ε½ . examples like End V , the ring of endomorphisms o