Function spaces for conditionally positive definite operator-valued kernels
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- by Georg Berschneider, Wolfgang zu Castell and Stefan J. Schrödl PDF
- Math. Comp. 81 (2012), 1551-1569 Request permission
Abstract:
The correspondence between reproducing kernel Hilbert spaces and positive definite kernels is well understood since Aronszajn’s work of the 1940s. The analog relation is less clear for conditionally positive definite kernels. The latter are widely used in approximation methods for scattered data, geostatistics, and machine learning. We consider this relation and provide two ways to construct a reproducing kernel Pontryagin space for operator-valued kernels.References
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Additional Information
- Georg Berschneider
- Affiliation: Institute for Mathematical Stochastics, Technische Universität Dresden, 01062 Dresden, Germany
- Email: georg.berschneider@tu-dresden.de
- Wolfgang zu Castell
- Affiliation: Department of Scientific Computing, Helmholtz Zentrum München, German Research Center for Environmental Health, Ingolstaedter Landstrasse 1, 85764 Neuherberg, Germany
- Email: castell@helmholtz-muenchen.de
- Stefan J. Schrödl
- Affiliation: Department of Scientific Computing, Helmholtz Zentrum München, German Research Center for Environmental Health, Ingolstaedter Landstrasse 1, 85764 Neuherberg, Germany
- Email: stefan.schroedl@gmx.net
- Received by editor(s): April 8, 2010
- Received by editor(s) in revised form: March 8, 2011
- Published electronically: October 18, 2011
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 81 (2012), 1551-1569
- MSC (2010): Primary 46C20, 41A63, 47A56; Secondary 41A05, 62M30, 62H30
- DOI: https://doi.org/10.1090/S0025-5718-2011-02552-4
- MathSciNet review: 2904590