| Project/Area Number |
09640166
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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 |
解析学
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| Research Institution | Niigata University |
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Principal Investigator |
HATORI Osamu Niigata University, Graduate School of Science and Technology, Associate Professor, 大学院・自然科学研究科, 助教授 (70156363)
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| Co-Investigator(Kenkyū-buntansha) |
WATANABE Keiichi Niigata University, Faculty of Scince Associate Professor, 理学部, 助教授 (50210894)
SAITO Kichi-suke Niigata University, Faculty of Scince, Professor, 理学部, 教授 (30018949)
IZUCHI Keiji Niigata University, Faculty of Scince, Professor, 理学部, 教授 (80120963)
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| Project Period (FY) |
1997 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 1998: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1997: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Keywords | commtative Banach algebra / locally compact abelian group / spectrum / Wiener-Pitt phenomenum / Fourier multiplier / operating function / Apostol algebra / decomposable operator / Wiener-Pitt現象 / 測度 / キーワード1局所コンパクトabel群 / キーワード2Wiener-Pitt現象 / キーワード3自然なスペクトル / キーワード4Fourier multiplier / キーワード5Apostol環 / キーワード6Douglas環 / キーワード7decomposable作用素 / キーワード8作用関数 |
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| Research Abstract |
We gave a sufficient condition for operating functions defined on a certain Banach function space to be only Lipschitz functions. Operating functions on non-trivial Banach function al-gebras or spaces need not be Lipschitz, but sutisifies strong continuity property. This means implicitly that it is hard to characterize the Gelfand space for a Banach function algebra in terms of operating functions.
Let M(G) be the measure algebra on a non-discrete locally compact abelian group G and NS(G) denote the set of all measures in M(G) with natura1 spectrum. Then, NS(G) is not closed under addition and NS(G) + L^1(G) = M(G) holds if G is not compact. Let M_0(G) be a closed subalgebra of M(G) which consisit of all measurs whose Fuorier-Stieltjes transforms vanish at infinity and NS_0(G) denotes the subset of M_0(G) whose element have natura1 spectra. If G is compact NS_0(G) coincides with the Apostol algebra of M_0(G), which is not the case for non-compact G.There exists a measure mu in NS(G) such that mu is not decomposable as an operator on L^1(G). In particular, NS(G)+ NS(G)+ NS(G) = M(G) holds.
The Apostol algebra of a Douglas algebra coincides with the algebra of all Q-continuous functions. Let H^* be the algebra of all bounded analytic functions on the open unit disk. Then NSH^*+ NSH^* = H^* holds, thus NSH^* is not closed under addition and it is rather large subset of H^*.
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