Functions operating on positive definite matrices and a theorem of Schoenberg
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- by Jens Peter Reus Christensen and Paul Ressel PDF
- Trans. Amer. Math. Soc. 243 (1978), 89-95 Request permission
Abstract:
We prove that the set of all functions $f: [ - 1, 1] \to [ - 1, 1]$ operating on real positive definite matrices and normalized such that $f(1) = 1$, is a Bauer simplex, and we identify its extreme points. As an application we obtain Schoenberg’s theorem characterising positive definite kernels on the infinite dimensional Hilbert sphere.References
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Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 243 (1978), 89-95
- MSC: Primary 15A48; Secondary 42A63
- DOI: https://doi.org/10.1090/S0002-9947-1978-0502895-2
- MathSciNet review: 502895