Harmonic maps and shift-invariant subspaces
Abstract
We investigate in detail the connection between harmonic maps from Riemann surfaces into the unitary group (n) and their Grassmannian models: these are families of shift-invariant subspaces of L2(S1,n). With the help of operator-theoretic methods we derive a criterion for finiteness of the uniton number which has a large number of applications discussed in the paper.
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