Rank one perturbations with infinitesimal coupling
Publication
, Journal Article
Kiselev, A; Simon, B
Published in: Journal of Functional Analysis
January 1, 1995
We consider a positive self-adjoint operator A and formal rank one perturbations B = A + α(φ, ·)φ, where φ ∈ H-2(A) but φ ∉ H-1 (A), with Hs(A) the usual scale of spaces. We show that B can be defined for such φ and what are essentially negative infinitesimal values of α. In a sense we will make precise, every rank one perturbation is one of three forms: (i) φ ∈ H-1(A), α ∈ R; (ii) φ ∈ H-1, α = ∞; or (iii) the new type we consider here. © 1995 Academic Press Limited.
Duke Scholars
Published In
Journal of Functional Analysis
DOI
EISSN
1096-0783
ISSN
0022-1236
Publication Date
January 1, 1995
Volume
130
Issue
2
Start / End Page
345 / 356
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Kiselev, A., & Simon, B. (1995). Rank one perturbations with infinitesimal coupling. Journal of Functional Analysis, 130(2), 345–356. https://doi.org/10.1006/jfan.1995.1074
Kiselev, A., and B. Simon. “Rank one perturbations with infinitesimal coupling.” Journal of Functional Analysis 130, no. 2 (January 1, 1995): 345–56. https://doi.org/10.1006/jfan.1995.1074.
Kiselev A, Simon B. Rank one perturbations with infinitesimal coupling. Journal of Functional Analysis. 1995 Jan 1;130(2):345–56.
Kiselev, A., and B. Simon. “Rank one perturbations with infinitesimal coupling.” Journal of Functional Analysis, vol. 130, no. 2, Jan. 1995, pp. 345–56. Scopus, doi:10.1006/jfan.1995.1074.
Kiselev A, Simon B. Rank one perturbations with infinitesimal coupling. Journal of Functional Analysis. 1995 Jan 1;130(2):345–356.
Published In
Journal of Functional Analysis
DOI
EISSN
1096-0783
ISSN
0022-1236
Publication Date
January 1, 1995
Volume
130
Issue
2
Start / End Page
345 / 356
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics