Journal article
SPECTRAL DUALITY FOR UNBOUNDED OPERATORS
Journal of operator theory, Vol.65(2), pp.325-353
03/01/2011
Abstract
We establish a spectral duality for certain unbounded operators in Hilbert space. The class of operators includes discrete graph Laplacians arising from infinite weighted graphs. The problem in this context is to establish a practical approximation of infinite models with suitable sequences of finite models which in turn allow (relatively) easy computations.
Let X be an infinite set and let H be a Hilbert space of functions on X with inner product <.,.> = <.,.>(H). We will be assuming that the Dirac masses delta(x), for x is an element of X, are contained in H. And we then define an associated operator Delta in H given by
(Delta v)(z) := <delta(x),v >(H).
Similarly, for every finite subset F subset of X, we get an operator Delta(F).
If F-1 subset of F-2 subset of ... is an ascending sequence of finite subsets such that U F-k = X, we are interested in the following two problems:
k is an element of N
(a) obtaining an approximation formula lim k ->infinity Delta(Fk) = Delta;
(b) establish a computational spectral analysis for the truncated operators Delta(F) in (a).
Details
- Title: Subtitle
- SPECTRAL DUALITY FOR UNBOUNDED OPERATORS
- Creators
- Dorin Ervin Dutkay - Univ Cent Florida, Dept Math, Orlando, FL 32816 USAPalle E. T Jorgensen - Univ Iowa, Dept Math, Iowa City, IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Journal of operator theory, Vol.65(2), pp.325-353
- Publisher
- THETA FOUNDATION
- ISSN
- 0379-4024
- eISSN
- 1841-7744
- Number of pages
- 29
- Language
- English
- Date published
- 03/01/2011
- Academic Unit
- Mathematics
- Record Identifier
- 9984241047102771
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