Schoenberg's Problem on Positive Definite Functions

1992/10/19 by Alexander Koldobsky, Koldobsky, Alexander · 1 citation
Mathematics · Physics and Astronomy · #Mathematics and Applications #Advanced Mathematical Theories and Applications #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.math/9210207

Abstract

If n ≥ 3, q>2 and β> 0 then the function exp(-(|x₁|^q+|x₂|^q+…+|x_n|^q)^β/q) is not positive definite. This result gives an answer to a question posed by I.J.~Schoenberg in 1938. This text is an authorized English translation of the paper published in Russian in Algebra and Analysis 3(1991), #3, p.78--85.

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