Mathematics – Functional Analysis
Scientific paper
2000-05-09
Mathematics
Functional Analysis
Proposition 2.1 revised. Remarks 2.15 and 2.16 added. 38 pages. To appear in Journal of Functional Analysis
Scientific paper
Given a self-adjoint operator $A:D(A)\subseteq\calH\to\calH$ and a continuous linear operator $\tau:D(A)\to\X$ with Range$ \tau'\cap\calH' ={0}$, $\X$ a Banach space, we explicitly construct a family $A^\tau_\Theta$ of self-adjoint operators such that any $A^\tau_\Theta$ coincides with the original $A$ on the kernel of $\tau$. Such a family is obtained by giving a Kre\u\i n-like formula where the role of the deficiency spaces is played by the dual pair $(\X,\X')$; the parameter $\Theta$ belongs to the space of symmetric operators from $\X'$ to $\X$. When $\X=\C$ one recovers the ``$\calH_{-2}$ -construction'' of Kiselev and Simon and so, to some extent, our results can be regarded as an extension of it to the infinite rank case. Considering the situation in which $\calH=L^2(\RE^n)$ and $\tau$ is the trace (restriction) operator along some null subset, we give various applications to singular perturbations of non necessarily elliptic pseudo-differential operators, thus unifying and extending previously known results.
No associations
LandOfFree
A Krein-Like Formula for Singular Perturbations of Self-Adjoint Operators and Applications does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Krein-Like Formula for Singular Perturbations of Self-Adjoint Operators and Applications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Krein-Like Formula for Singular Perturbations of Self-Adjoint Operators and Applications will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-214758