| Project/Area Number |
17540139
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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 | Hokkaido University |
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Principal Investigator |
NAKAZI Takahiko Hokkaido University, Fac.of Sci., Professor (30002174)
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| Co-Investigator(Kenkyū-buntansha) |
HAYASHI Mikihiro Hokkaido University, Far.of Sci, Professor (40007828)
TACHIZAWA Kazuya Hokkaido University, Fac.of Sci, Professor (80227090)
IZUCHI Keiji Niigata University, Grad.School of Science and Technology, Professor (80120963)
SETO Michio Simane University, Interdisciplinary Faculty of Science and Engineering, Lecturer (30398953)
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| Project Period (FY) |
2005 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥3,960,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥360,000)
Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2005: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Keywords | Hardy space / several variables / invariant subspace / Toeplitz operator / shift operator / wandering subspace / cross commutator / 多変数 / hyponormal作用素 / スペクトル / Hankel作用素 / 内部関数 / ハーディ空間 / 不動点 / イデアル |
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| Research Abstract |
We study an operator on an invariant, subspace in Hardy space H^2(D^2) on the bidisc. The research is strongly related to the structure of an invariant subspace M. The following are studied in this project.
(1) Under some condition, we describe operators which commute with doubly commuting compressed shifts on the orthogonal complement N of M. Moreover applying it to an interpolation problem for holomorphic functions on the bidisc, we prove a theorem of Nevanlinna-Pick type.
(2) We define wandering subspaces in M and N. They are important small parts of M and N, respectively. We make clear relations between a wandering subspace of M and one of N.
(3) We consider two analytic Toeplitz operators restricted to an invariant subspace M. We study M when the cross commutator of them is zero. Then we describe completely M for some special analytic Toeplitz operators.
(4) When the lattice of invariant subspaces of a Toeplitz operator is contained in the intersection of lattices of invariant subspaces for analytic Toeplitz operator, we show the Toeplitz operator is analytic. Moreover we consider C^*-valued one variable Hardy space and two shifts on it. We give necessary and sufficient condition for unitary equivalence of C^* algebras on two some invariant subspaces.
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