Eighth Mississippi State - UAB Conference on Differential Equations and
Computational Simulations.
Electron. J. Diff. Eqns., Conference 19 (2010), pp. 31-36.

Title: Models of learning and the polar decomposition of
       bounded linear operators

Authors: Fernanda Botelho (The Univ. of Memphis, TN, USA)
         Annita Davis     (The Univ. of Memphis, TN, USA)
 
Abstract: 
 We study  systems of differential equations in
 $\mathcal{B}(\mathcal{H})$, the space of all bounded linear
 operators on a separable complex Hilbert space $ \mathcal{H} $
 equipped with the  operator norm. These systems  are infinite
 dimensional generalizations of mathematical models of learning.
 We use the polar decomposition of operators to find an explicit
 form for solutions. We also discuss the standard questions of
 existence and uniqueness of local and global solutions, as well
 as their long-term behavior.

Published September 25, 2010.
Math Subject Classifications: 34G20, 47J25.
Key Words: Nonlinear systems; learning models; 
  polar decomposition of operators.