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Separability of reproducing kernel spaces


Authors: Houman Owhadi and Clint Scovel
Journal: Proc. Amer. Math. Soc. 145 (2017), 2131-2138
MSC (2010): Primary 46E22
DOI: https://doi.org/10.1090/proc/13354
Published electronically: October 27, 2016
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Abstract: We demonstrate that a reproducing kernel Hilbert or Banach space of functions on a separable absolute Borel space or an analytic subset of a Polish space is separable if it possesses a Borel measurable feature map.


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Additional Information

Houman Owhadi
Affiliation: Department of Computing and Mathematical Sciences, California Institute of Technology, MC 9-94, Pasadena, California 91125
Email: owhadi@caltech.edu

Clint Scovel
Affiliation: Department of Computing and Mathematical Sciences, California Institute of Technology, MC 9-94, Pasadena, California 91125
Email: clintscovel@gmail.com

DOI: https://doi.org/10.1090/proc/13354
Received by editor(s): July 13, 2015
Received by editor(s) in revised form: March 3, 2016, May 31, 2016, and July 5, 2016
Published electronically: October 27, 2016
Communicated by: Mark M. Meerschaert
Article copyright: © Copyright 2016 American Mathematical Society