English

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.

Keywords

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

R2 v1 2026-06-21T14:01:40.893Z