2004 Fiscal Year Final Research Report Summary
The Study of Operator monotone Functions by Analytic Continuation and Its Application
| Project/Area Number |
14540180
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Fukuoka University of Education |
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Principal Investigator |
UCHIYAMA Mitsuru Fukuoka University of Education, Mathematics, Professor, 教育学部, 教授 (60112273)
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| Co-Investigator(Kenkyū-buntansha) |
KOSAKI Hideki Kyushu University, Mathematics, Professor, 大学院・数理学研究科, 教授 (20186612)
HARA Takuya Fukuoka University of Education, Mathematics, Associate Professor, 教育学部, 助教授 (50263984)
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| Project Period (FY) |
2002 – 2004
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| Keywords | Hilbert space / Linear operator / Positive semi-definite operator / Operator monotone function / Orthogonal polynomials / Majorization |
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| Research Abstract |
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.
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