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.