Study of operators on spaces of analytic functions and the space of bounded analytic functions
| Project/Area Number |
24540164
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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 |
Basic analysis
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| Research Institution | Niigata University |
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Principal Investigator |
IZUCHI Keiji 新潟大学, 自然科学系, フェロ- (80120963)
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| Co-Investigator(Kenkyū-buntansha) |
OHNO Syuichi 日本工業大学, 工学部, 准教授 (20265367)
HATORI Osamu 新潟大学, 自然科学系, 教授 (70156363)
IZUCHI Kouhei 山口大学, 教育学部, 講師 (90451434)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2012: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 有界解析関数 / 極大イデアル空間 / 閉イデアル / ハーデイ空間 / 不変部分空間 / 内部関数 / 荷重合成作用素 / 弧状連結成分 / 有界解析関数空間 / 有界調和関数空間 / 作用素ノルム位相 / 本質作用素ノルム位相 / 多変数ハーデイ空間 / 合成作用素の連結成分 / 国際研究者交流：フィンランド / 国際情報交換：中国 / 国際情報交換：韓国 |
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| Outline of Final Research Achievements |
It is determined the structure of closed ideals and countably generated closed ideals whose common zero sets in the maximal ideal space of the Banach algebra of bounded analytic functions on the open unit disk are contained in the union set of nontrivial Gleason parts. It is also determined the path connected components of the weighted composition operators on the space of bounded analytic functions with respect to the operator norm and essential operator norm topologies. Moreover the path connected components are determined on the space of bounded harmonic functions and on the disk algebra.
The study of the Hardy space on the bidisk, some backward shift invariant subspaces having rank 1 cross commutator are described. It is also determined the ranks of Rudin type (backward) shift invariant subspaces associated with sequences of inner functions satisfying some conditions,
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Report
(4 results)
Research Products
(62 results)
