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arXiv · 1812.09379

Harmonic maps and shift-invariant subspaces

Alexandru Aleman·Rui Pacheco·John C. Wood
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Abstract

We investigate in detail the connection between harmonic maps from Riemann surfaces into the unitary group $\U(n)$ and their Grassmannian models: these are families of shift-invariant subspaces of $L^2(S^1,\C^n)$. 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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Alexandru Aleman, Rui Pacheco, John C. Wood. 2018-12-21. Harmonic maps and shift-invariant subspaces. https://arxiv.org/abs/1812.09379

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