半正则双正交对与广义Riesz基
Semi-regular biorthogonal pairs and generalized Riesz bases
摘要：
本文定义了半正则双正交对的概念，它是文献\cite{hiroshi1}中正则双正交对的推广，并证明了如果$(\{ ϕ_{n} \} , \{ ψ_{n} \})$是半正则双正交对，则$\{ ϕ_{n} \}$和$\{ ψ_{n} \}$是广义Riesz基.该结果改进了参考文献\cite{h-t, hiroshi1, h-t2}在常规情况下的结果。
英文摘要：
In this paper we define the notion of semi-regular biorthogonal pairs what is a generalization of regular biorthogonal pairs in Ref. \cite{hiroshi1} and show that if $(\{ ϕ_{n} \} , \{ ψ_{n} \})$ is a semi-regular biorthogonal pair, then $\{ ϕ_{n} \}$ and $\{ ψ_{n} \}$ are generalized Riesz bases. This result improves the results of Ref. \cite{h-t, hiroshi1, h-t2} in the regular case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
