Boundary Conditions for Singular Perturbations of Self-Adjoint Operators
| dc.creator | Posilicano, Andrea | |
| dc.date | 2001-02-02 | |
| dc.date | 2002-05-23 | |
| dc.date.accessioned | 2026-07-07T04:39:57Z | |
| dc.date.available | 2026-07-07T04:39:57Z | |
| dc.description | Let $A:D(A)\subseteq\H\to\H$ be an injective self-adjoint operator and let $τ:D(A)\to\X$, X a Banach space, be a surjective linear map such that $\|τϕ\|_\X\le c \|Aϕ\|_\H$. Supposing that \text{\rm Range}$ (τ')\cap\H' =\{0\}$, we define a family $A^τ_Θ$ of self-adjoint operators which are extensions of the symmetric operator $A_{|\{τ=0\}.}$. Any $ϕ$ in the operator domain $D(A^τ_Θ)$ is characterized by a sort of boundary conditions on its univocally defined regular component $\phireg$, which belongs to the completion of D(A) w.r.t. the norm $\|Aϕ\|_\H$. These boundary conditions are written in terms of the map $τ$, playing the role of a trace (restriction) operator, as $τ\phireg=ΘQ_ϕ$, the extension parameter $Θ$ being a self-adjoint operator from X' to X. The self-adjoint extension is then simply defined by $A^τ_Θϕ:=A \phireg$. The case in which $Aϕ=T*ϕ$ is a convolution operator on LD, T a distribution with compact support, is studied in detail. | |
| dc.description | Revised version. To appear in Operator Theory: Advances and Applications, vol. 132 | |
| dc.identifier | https://arxiv.org/abs/math/0102018 | |
| dc.identifier | http://arxiv.org/abs/math/0102018 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60879 | |
| dc.subject | Functional Analysis | |
| dc.subject | Mathematical Physics | |
| dc.title | Boundary Conditions for Singular Perturbations of Self-Adjoint Operators | |
| dc.type | text |