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On conditionally positive definite dot product kernels

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Abstract

Let m and n be fixed, positive integers and

a space composed of real polynomials in m variables. The authors study functions f: ℝ → ℝ which map Gram matrices, based upon n points of ℝm, into matrices, which are nonnegative definite with respect to

. Among other things, the authors discuss continuity, differentiability, convexity, and convexity in the sense of Jensen, of such functions.

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Authors and Affiliations

  1. Departamento de Matemática, ICMC-USP — São Carlos, Caixa Postal 668, 13560-970, São Carlos SP, Brasil

    V. A. Menegatto & Ana P. Peron

  2. ICE-DMC, Universidade Federal de Itajubá, Caixa Postal 50, 37500-903, Itajubá MG, Brasil

    C. P. Oliveira

Authors
  1. V. A. Menegatto
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  2. C. P. Oliveira
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  3. Ana P. Peron
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Corresponding author

Correspondence to V. A. Menegatto.

Additional information

The first and third authors are partially supported by PROCAD-CAPES, Grant #0092/01-0

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Menegatto, V.A., Oliveira, C.P. & Peron, A.P. On conditionally positive definite dot product kernels. Acta. Math. Sin.-English Ser. 24, 1127–1138 (2008). https://doi.org/10.1007/s10114-007-6227-4

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  • DOI: https://doi.org/10.1007/s10114-007-6227-4

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