Scholarlink

<p>We provide quantitative improvements to the Berezin-Li-Yau inequality and the Kröger inequality, in ℝ<sup><i>n</i></sup>, <i>n</i> ⩾ 2. The improvement on the Kröger inequality resolves an open question raised by Weidl from 2006. The improvements allow us to show that for any open bounded domains, there are infinitely many Dirichlet eigenvalues satisfying Pólya’s conjecture if <i>n</i> ⩾ 3, and infinitely many Neumann eigenvalues satisfying Pólya’s conjecture if <i>n</i> ⩾ 5 and the Neumann spectrum is discrete.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The improved Berezin-Li-Yau inequality and Kröger inequality and consequences

  • 期刊论文

  • 发表日期：

    2026年4月21日

查看全文
  • Zaihui Gan,
  • Renjin Jiang,
  • Fanghua Lin

摘要

We provide quantitative improvements to the Berezin-Li-Yau inequality and the Kröger inequality, in ℝn, n ⩾ 2. The improvement on the Kröger inequality resolves an open question raised by Weidl from 2006. The improvements allow us to show that for any open bounded domains, there are infinitely many Dirichlet eigenvalues satisfying Pólya’s conjecture if n ⩾ 3, and infinitely many Neumann eigenvalues satisfying Pólya’s conjecture if n ⩾ 5 and the Neumann spectrum is discrete.