The Study of Operator monotone Functions by Analytic Continuation and Its Application

算子单调函数的解析延拓研究及其应用

• 批准号: 14540180
• 负责人: UCHIYAMA Mitsuru
• 金额: $ 2.11万
• 依托单位: Fukuoka University of Education
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540180/
• 关键词: Hilbert space; Linear operator; Positive semi-definite operator; Operator monotone function; Orthogonal polynomials; Majorization; majorization; 直行多項式系; 自己共役作用素

We have almost achieved the purpose of this research project, that is, constructing new family of operator monotone functions with analytic continuation method. Actually we got the following- if a real monic polynomial has only real zeros, then the inverse function of the increasing part is operator monotone, and that if it has complex zeros, then the inverse function is semi-operator monotone. We have shown this result in the paper published from Transactions of American Mathematical Society We conjectured originally this problem and solved it with analytic continuation method. We hope this will be applied to orthogonal polynomials which are very important in many fields of mathematics.

我们已经基本达到了本研究项目的目的，即用解析延拓法构造新的算子单调函数族。实际上我们得到了以下结论：如果实数多项式只有实数零点，那么增加部分的反函数是算子单调，如果它有复数零点，那么反函数是半算子单调。我们在《美国数学会汇刊》上发表的论文中已经展示了这个结果。我们最初猜想这个问题，并用解析连续法解决了它。我们希望这能够应用于在许多数学领域非常重要的正交多项式。

项目成果

K.Tanahashi, M.Uchiyama: "On Schwarz type inequalities"Proc.Amer.Math.Soc.. 131・8. 2549-2552 (2003)

K.Tanahashi、M.Uchiyama：“论 Schwarz 型不等式”Proc.Amer.Math.Soc. 131・8（2003）。

Operator means and their norms

经营手段及其规范

• 发表时间: 2004
• 期刊: ASPM"Operator Algebras and Applications"(Proc.of US-Japan Seminar)(Math.Soc.Japan) 38
• 作者: F.Hiai;H.Kosaki
• 通讯作者: H.Kosaki

Proofs of Korovkin's theorems via inequalities.

通过不等式证明科洛夫金定理。

• 发表时间: 2003
• 期刊: Amer.Math.Monthly 110・4
• 作者: H.Hamada;M.Uchiyama
• 通讯作者: M.Uchiyama

Operator monotone functions and operator inequality

算子单调函数和算子不等式

• 发表时间: 2002
• 期刊: Sugaku (Japanese Math.Soc.) 54
• 作者: M.Uchiyama

Means of Hilbert space operators

• 发表时间: 2003
• 作者: 日合 文雄;幸崎 秀樹