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Harmonic maps and shift-invariant subspaces

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arxiv 1812.09379 v3 pith:S7SPHATX submitted 2018-12-21 math.FA math.DG

Alexandru Aleman , Rui Pacheco , John C. Wood This is my paper · ORCID
classification math.FAmath.DG
keywords harmonicmapsnumbershift-invariantsubspacesapplicationsconnectioncriterion
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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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Cited by 1 Pith paper

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  1. Symmetric shift-invariant subspaces and harmonic maps

    math.FA 2019-08 accept novelty 6.0 of 10

    A k-symmetric shift-invariant subspace corresponds exactly to a filtration of invariant subspaces, yielding new general forms for extended solutions and a method to reverse the known construction of harmonic maps from...

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