Journal of Mathematics and Statistics

STATIONARY CONNECTED CURVES IN HILBERT SPACES

Raed Hatamleh, Ahmad Qazza and Hatim Migdadi

DOI : 10.3844/jmssp.2014.262.266

Journal of Mathematics and Statistics

Volume 10, Issue 2

Pages 262-266

Abstract

In this article the structure of non-stationary curves which are stationary connected in Hilbert space is studied using triangular models of non-self-adjoint operator. The concept of evolutionary representability plays here an important role. It is proved that if one of two curves in Hilbert space is evolutionary representable and the curves are stationary connected, then another curve is evolutionary representable too. These curves are studied firstly. The structure of a cross-correlation function in the case when operator, defining the evolutionary representation, has one-dimensional non-Hermitian subspace (the spectrum is discreet and situated in the upper complex half-plane or has infinite multiplicity at zero (Volterra operator)) is studied.

Copyright

© 2014 Raed Hatamleh, Ahmad Qazza and Hatim Migdadi. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.