Research Article Open Access

STATIONARY CONNECTED CURVES IN HILBERT SPACES

Raed Hatamleh1, Ahmad Qazza1 and Hatim Migdadi1
  • 1 Jadara University, Jordan

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.

Journal of Mathematics and Statistics
Volume 10 No. 2, 2014, 262-266

DOI: https://doi.org/10.3844/jmssp.2014.262.266

Submitted On: 6 March 2014 Published On: 17 May 2014

How to Cite: Hatamleh, R., Qazza, A. & Migdadi, H. (2014). STATIONARY CONNECTED CURVES IN HILBERT SPACES. Journal of Mathematics and Statistics, 10(2), 262-266. https://doi.org/10.3844/jmssp.2014.262.266

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Keywords

  • Stationary Connectedness
  • Infinitesimal Correlation Matrix
  • Triangular Operator Model
  • Channel Operator Element