Scholarlink

<p>In this work we prove analogues of Bessel inequality and Riesz–Fischer theorem in Hilbert spaces. We apply our generalized Bessel inequality to the Hilbert spaces associated with the Normal, Beta, Gamma and several discrete probability distributions to show how to generate certain types of inequalities for special functions systematically. In particular, from the Normal distribution we obtain inequalities for certain <i>q</i>-special functions; from the Beta distribution we derive inequalities for various hypergeometric functions; and from discrete distributions we establish inequalities for Dirichlet series.</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

On almost orthogonal series

  • 期刊论文

  • 发表日期：

    2026年1月5日

查看全文
  • Ruiming Zhang

摘要

In this work we prove analogues of Bessel inequality and Riesz–Fischer theorem in Hilbert spaces. We apply our generalized Bessel inequality to the Hilbert spaces associated with the Normal, Beta, Gamma and several discrete probability distributions to show how to generate certain types of inequalities for special functions systematically. In particular, from the Normal distribution we obtain inequalities for certain q-special functions; from the Beta distribution we derive inequalities for various hypergeometric functions; and from discrete distributions we establish inequalities for Dirichlet series.