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<p>We prove a criterion for the positive definiteness of a quadratic functional on a Hilbert space, and give its application to proving sufficient conditions for a weak second-order minimum in the simplest problem of the classical calculus of variations.</p>

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Criterion for the Positive Definiteness of a Quadratic Functional and Its Application

  • 期刊论文

  • 发表日期：

    2025年11月24日

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  • E. R. Avakov,
  • G. G. Magaril-Il’yaev

摘要

We prove a criterion for the positive definiteness of a quadratic functional on a Hilbert space, and give its application to proving sufficient conditions for a weak second-order minimum in the simplest problem of the classical calculus of variations.