It is shown that the operators associated with the perturbed wave equation in IR n and with the elliptic operators with an indeenite weight function and mildly varying coeecients on IR n are similar to a selfadjoint operator in a Hilbert space. These operators have the whole IR as the spectrum. It is shown that they are positive operators in corresponding Krein spaces, and the whole problem is ...

For pairs of density operators on nite dimensional Hilbert spaces we deene partial delities, prove their concavity and other properties. Partial delities characterize equivalence classes which are partially ordered in a natural way.

We present an efficient algorithm using the Hilbert Transform for estimating the delay of the BOLD response to neuronal stimulation. With minimal additional computations, the algorithm estimates parameters generated in the widely used cross-correlation method and simplifies the interpolation required to estimate the response delay from the cross-correlation function. We examined errors in the H...

In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...

The Hilbert function of a module over a positively graded algebra is of quasi-polynomial type (Hilbert–Serre). We derive an upper bound for its grade, i. e. the index from which on its coefficients are constant. As an application, we give a purely algebraic proof of an old combinatorial result (due to Ehrhart, McMullen and Stanley). 1. HILBERT QUASIPOLYNOMIALS Let K be a field, and R a positive...