Harmonic maps and shift-invariant subspaces

Alexandru Aleman; Rui Pacheco; John C. Wood

Harmonic maps and shift-invariant subspaces

Functional Analysis 2019-10-16 v3 Differential Geometry

Authors: Alexandru Aleman , Rui Pacheco , John C. Wood

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.

Keywords

harmonic maps grassmannian varieties invariant subspace theory

Cite

@article{arxiv.1812.09379,
  title  = {Harmonic maps and shift-invariant subspaces},
  author = {Alexandru Aleman and Rui Pacheco and John C. Wood},
  journal= {arXiv preprint arXiv:1812.09379},
  year   = {2019}
}

Comments

Treatment of Grassmannian model clarified and relation with work of M. Guest added

Harmonic maps and shift-invariant subspaces

Abstract

Keywords

Cite

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