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Publications
Differential equations in Schatten classes of operators

# Differential equations in Schatten classes of operators,10.1007/s00605-009-0114-2,Monatshefte Fur Mathematik,Fernanda Botelho,James E. Jamison

Differential equations in Schatten classes of operators
We study a system of differential equations in Schatten classes of operators, $${\mathcal{C}_p(\mathcal{H})\,(1 \leq p$${\mathcal{H}} a separable complex Hilbert space. The systems considered are infinite dimensional generalizations of mathematical models of unsupervised learning. In this new setting, we address the usual questions of existence and uniqueness of solutions. Under some restrictions on the spectral properties of the initial conditions, we explicitly solve the system. We also discuss the long-term behavior of solutions.