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On some positive definite functions

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Abstract

We study the function \((1 - \Vert x\Vert )/ (1 - \Vert x\Vert ^r),\) and its reciprocal, on the Euclidean space \(\mathbb {R}^n,\) with respect to properties like being positive definite, conditionally positive definite, and infinitely divisible.

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Acknowledgments

The work of the first author is supported by a J. C. Bose National Fellowship, and of the second author by an SERB Women Excellence Award. The first author was a Fellow Professor at Sungkyunkwan University in the summer of 2014.

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Authors and Affiliations

  1. Indian Statistical Institute, New Delhi, 110016, India

    Rajendra Bhatia & Tanvi Jain

  2. Sungkyunkwan University, Suwon, 440-746, Korea

    Rajendra Bhatia

Authors
  1. Rajendra Bhatia
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  2. Tanvi Jain
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Correspondence to Rajendra Bhatia.

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Bhatia, R., Jain, T. On some positive definite functions. Positivity 19, 903–910 (2015). https://doi.org/10.1007/s11117-015-0334-8

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  • DOI: https://doi.org/10.1007/s11117-015-0334-8

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