Fernanda Botelho, Annita Davis
Abstract:
We study systems of differential equations in
, the space of all bounded linear
operators on a separable complex Hilbert space
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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