On a connection between Naimark's dilation theorem, spectral representations, and characteristic functions Mishko Mitkovski 47A2047A4530J99Naimark's dilation theoremgeneralized spectral measurecharacteristic functionrank-one perturbations of a partial isometry We give a Herglotz-type representation of an arbitrary generalized spectral measure. As an application, a new proof of the classical Na\u\i mark'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. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4175 10.1512/iumj.2011.60.4175 en Indiana Univ. Math. J. 60 (2011) 507 - 516 state-of-the-art mathematics http://iumj.org/access/