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In this paper we use a linear programming technique to get estimates from below for the minimal energy with respect to Gaussian kernels. Our proof requires taking care of behavior of coefficients in the expansion of a Gaussian in a certain specific orthogonal basis. In particular, contrary to the common linear programming situation, those coefficients are not positive and cannot be neglected when estimating from below.

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A Linear Programming Bound in a Sign-alternating Case

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  • 发表日期：

    2026年

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  • Alexander Reznikov

摘要

In this paper we use a linear programming technique to get estimates from below for the minimal energy with respect to Gaussian kernels. Our proof requires taking care of behavior of coefficients in the expansion of a Gaussian in a certain specific orthogonal basis. In particular, contrary to the common linear programming situation, those coefficients are not positive and cannot be neglected when estimating from below.