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Symmetric shift-invariant subspaces and harmonic maps · arXivDesk

1908.01557Aug 5, 2019The original preprint `Harmonic maps and shift-invariant subspaces' was splitted in two. This is the second part. arXiv admin note: substantial text overlap with arXiv:1812.09379

Symmetric shift-invariant subspaces and harmonic maps

Alexandru Aleman, Rui Pacheco, John C. Wood

Functional Analysis Complex Variables Differential Geometry

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Abstract

The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an important class of harmonic maps into symmetric and $k$ -symmetric spaces. In particular, we obtain new general forms for such symmetric shift-invariant subspaces and for the corresponding extended solutions.

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The paper addresses: Symmetric shift-invariant subspaces and harmonic maps.
The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space.

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Author comment: The original preprint `Harmonic maps and shift-invariant subspaces' was splitted in two. This is the second part. arXiv admin note: substantial text overlap with arXiv:1812.09379