2007 Fiscal Year Final Research Report Summary
Research of a Hardy space on a polydisc
| 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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| Keywords | Hardy space / several variables / invariant subspace / Toeplitz operator / shift operator / wandering subspace / cross commutator |
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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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[Book] 解析学百科I 古典調和解析2008
Author(s)
薮田 公三, 中路 貴彦, 佐藤 圓治, 田中 仁, 宮地 晶彦
Total Pages
400
Publisher
朝倉書店
Description
「研究成果報告書概要(和文)」より
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