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We consider an analytic function from \(\mathbb {R}^n\) to \(\mathbb {R}\) and provide some sufficient conditions involving homogeneous polynomials with respect to some family of dilations ensuring that the function presents a strict local minimum at some point. For a polynomial function, we show how to use Tarski-Seidenberg theorem or Sturm theorem to investigate the same issue.

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High-Order Conditions for an Analytic Function to Be Locally Positive Definite

  • 会议论文

  • 发表日期：

    2025年

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  • Lionel Rosier

摘要

We consider an analytic function from \(\mathbb {R}^n\) to \(\mathbb {R}\) and provide some sufficient conditions involving homogeneous polynomials with respect to some family of dilations ensuring that the function presents a strict local minimum at some point. For a polynomial function, we show how to use Tarski-Seidenberg theorem or Sturm theorem to investigate the same issue.