| Project/Area Number |
25400204
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Nara University of Education |
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Principal Investigator |
Ito Naoharu 奈良教育大学, 教育学部, 教授 (90246661)
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| Research Collaborator |
Wimmer H. K. Universität Würzburg
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 行列多項式 / 高階差分方程式 / 作用素多項式 / 自己反転多項式 / 数域 / 内数域半径 / 固有値 / 近似固有値 / 正規近似固有値 / 自己反転行列多項式 / Enestroem-Kakeya型定理 / 国際情報交換（ドイツ） / Enestroem-Kakeya型の定理 |
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| Outline of Final Research Achievements |
The spectrum of a class of self-inversive matrix polynomials was studied. It was shown that the characteristic values are normal, semisimple and lie on the unit circle if the inner radius of an associated matrix polynomial is greater than one. Then, we investigated higher order systems of linear difference equations where the associated characteristic matrix polynomial is selfinversive. We showed that all solutions are bounded if the inner radius is greater than one. In the case of matrix polynomials with positve definite coefficient matrices we derived a computable lower bound for the inner radius and we obtain a criterion for stable boundedness. Next, Hilbert space operator polynomials with self-inversive structure were studied. It was shown that if the inner numerical radius of an associated polynomial is greater than or equal to one then the spectrum lies on the unit circle and consists of normal approximate characteristic values.
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