Geometric Perspectives on Reproducing Kernels

Daniel Beltiţǎ () and José E. Galé ()
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Daniel Beltiţǎ: Institute of Mathematics “Simion Stoilow” of the Romanian Academy
José E. Galé: Universidad de Zaragoza and IUMA

Chapter 7 in Operator Theory, 2015, pp 127-148 from Springer

Abstract: Abstract It is shown how reproducing kernels, in a wide class, define in a very natural manner differential geometric objects like linear connections, covariant derivatives, and curvatures. The correspondence from kernels to connections is achieved through a pullback operation from the tautological universal bundle, using a suitable classifying morphism for the given kernel. The theory is illustrated by several examples including classical kernels in function spaces, kernels occurring in dilation theory for completely positive maps, and kernels on homogeneous vector bundles.

Keywords: Vector Bundle; Covariant Derivative; Connection Form; Complex Hilbert Space; Linear Connection (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0667-1_62

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DOI: 10.1007/978-3-0348-0667-1_62

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