1996 Fiscal Year Final Research Report Summary
Functional analysis and applications
| Project/Area Number |
08304011
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 総合 |
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| Research Field |
解析学
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| Research Institution | HIROSHIMA UNIVERSITY |
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Principal Investigator |
OHARU Shinnosuke Hiroshima-U., Mathematics, Professor, 理学部, 教授 (40063721)
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| Co-Investigator(Kenkyū-buntansha) |
TAKENAKA Sigeo Okayama Scinece U., Mathemathics, Professor, 理学部, 教授 (80022680)
YABUTA Kozo Nara womans U., Mathematics, Professor, 理学部, 教授 (30004435)
NAKAZI Takahiko Hokkaido U., Mathematics, Professor, 理学部, 教授 (30002174)
OHYA Masanori Tokyo Science U., Mathematics, Professor, 理工学部, 教授 (90112896)
KOMATSU Hikosaburo Tokyo Science U., Mathematics, Professor, 理学部, 教授 (40011473)
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| Project Period (FY) |
1996
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| Keywords | Hardy space / Toeplitz operator / Littlewood-Paley operator / evolution operator / nonlinear evolution problem / pseudo-differential operator / information dynamics / stable stochastic field |
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| Research Abstract |
Functional analysis is a diverse field and a great number of results on a variety of mathematical problems arising in the current mathematical sciences have been produced. In this research project it was aimed at making a significant contribution to the studies in functional analysis and its applications. The emphasis was layd on was function algebra, operator theory, theoretical development of nonlinear analysis, detailed freatments of mathematical models involving differential equations, generalized functions with applications to physics, and information theory based on operator algebra.
1.Inportand results on outer functions, weighted Hardy spaces, Toeplitz operators and invariant subspaces were obtained and Littlewood-Paley operators were investigated in new aspects.
2.In consideration of nonlinear problems arising in various mathematical models, an extensive study of evolution operators as well as its applications to those problems was made with the aid of the newest results on infi
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nite dimensional dynamical systems, pde's and numerical analysis.
3.Generalized functions were treated in terms of pseudo-differential operator theory, Toeplitz operator and generalized solutions of differential equations.
4.By means of new methods invented in functional analysis and stochastic calculus, theory of information dynamics was advanced. Extensive studies of various problems on boundary domains were made interms of complexity.
5.New results on determinism in stable stochastic fields were obtained and infinitely decomposable processes were investigated in various aspects.
A great deal of progress has been constantly made in functiona analysis and its applications. In order to pursue such studies, effective research collaboration with specialists in the related fields is particularly important. Owing to the grant-in-aid, most of the aimed results were obtained. In particular, an international conference on evolution equations and their applications to technolog was held with the participation of leading scientists in those fields and this support is greatly appreciated. Less
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