Abstract
We have defined in the previous chapter a category of admissible spaces V that drive the construction of groups of diffeomorphisms as flows associated to ordinary differential equations with velocities in V. We now show how such spaces can be explicitly constructed, focusing on Hilbert spaces. This construction is fundamental, because it is intimately related to computational methods involving flows of diffeomorphisms. We will in particular introduce the notion of reproducing kernels associated to an admissible space, which will provide our main computational tool. We introduce this in the next section.
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© 2010 Springer Berlin Heidelberg
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Younes, L. (2010). Building Admissible Spaces. In: Shapes and Diffeomorphisms. Applied Mathematical Sciences, vol 171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12055-8_9
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DOI: https://doi.org/10.1007/978-3-642-12055-8_9
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12054-1
Online ISBN: 978-3-642-12055-8
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