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

Models of learning and the polar decomposition of bounded linear operators

Fernanda Botelho, Annita Davis

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.

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Fernanda Botelho
The University of Memphis, Mathematical Sciences Dept.
Dunn Hall 373, 3721 Norriswood St.
Memphis, TN 38152-3240, USA
email: mbotelho@memphis.edu
Annita Davis
The University of Memphis, Mathematical Sciences Dept.
Dunn Hall 373, 3721 Norriswood St.
Memphis, TN 38152-3240, USA
email: adavis2@memphis.edu

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