On a connection between Naimark's dilation theorem, spectral representations, and characteristic functions
Functional Analysis
2009-10-22 v1 Complex Variables
Spectral Theory
Abstract
We give a Herglotz-type representation of an arbitrary generalized spectral measure. As an application, a new proof of the classical Naimark's dilation theorem is given. The same approach is used to describe the spectrum of all unitary rank-one perturbations of a given partial isometry.
Cite
@article{arxiv.0910.4140,
title = {On a connection between Naimark's dilation theorem, spectral representations, and characteristic functions},
author = {Mishko Mitkovski},
journal= {arXiv preprint arXiv:0910.4140},
year = {2009}
}
Comments
8 pages