Abstract
We investigate the interaction between the existence of reproducing kernels on infinite-dimensional Hermitian vector bundles and the positivity properties of the corresponding bundles. The positivity refers to the curvature form of certain covariant derivatives associated to reproducing kernels on the vector bundles under consideration. The values of the curvature form are Hilbert space operators, and its positivity is thus understood in the usual sense from operator theory.
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© 2016 Springer International Publishing Switzerland
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Beltiţă, D., Galé, J.E. (2016). Reproducing Kernels and Positivity of Vector Bundles in Infinite Dimensions. In: de Jeu, M., de Pagter, B., van Gaans, O., Veraar, M. (eds) Ordered Structures and Applications. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-27842-1_5
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DOI: https://doi.org/10.1007/978-3-319-27842-1_5
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-27840-7
Online ISBN: 978-3-319-27842-1
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