TY - JOUR
AU - Hatamleh, Raed
AU - Qazza, Ahmad
AU - Migdadi, Hatim
PY - 2014
TI - STATIONARY CONNECTED CURVES IN HILBERT SPACES
JF - Journal of Mathematics and Statistics
VL - 10
IS - 2
DO - 10.3844/jmssp.2014.262.266
UR - https://thescipub.com/abstract/jmssp.2014.262.266
AB - 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.