2003 Fiscal Year Final Research Report Summary
THE RESARCH OF PERATORS ON FUNCTION SPACES BY THE METHOD TO HARMONIC ANALYSIS AND RELATED ANALYSIS
| Project/Area Number |
14540150
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | YAMAGATA UNIVERSITY |
|---|
Principal Investigator |
SATO Eiji YAMAGATA UNIV., FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (80107177)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
MIZUHARA Takahiro YAMAGATA UNIV., FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (80006577)
MORI Seiki YAMAGATA UNIV., FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (80004456)
OKAYASU Takateru YAMAGATA UNIV., FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (60005775)
KAWAMURA Shinzo YAMAGATA UNIV., FACULTY OF SCIENCE, PROFESSOR, 理学部, 教授 (50007176)
仲田 正躬 山形大学, 理学部, 教授 (20007173)
|
|---|
| Project Period (FY) |
2002 – 2003
|
| Keywords | Lorentz space / Hankel transform / k-hyponormal operators / deficiency / commutator / Juia set / probability densety function / Mobious transformation |
|---|
| Research Abstract |
Our purpose of this research is to study the properties of operators on function spaces by the method of harmonic analysis and related analysis. Our investigators did the research at each special point. The content is as follows:
Sato studied the generalization of the relation between some operators of Hankel transforms on the positive numbers and the operators of Jacobi orthogonal system on (0,\pi). Okayasu investigated the structure of isometries on a function space and the Korovkin type linear approximation of them by contractions. Besides, he investigated the maximum part of a tuple of operators on a Hilbert space for which an indicated operator inequality holds. Mori researched about a problem of constructions of algebraically nondegenerate meromorphic mappings f of complex spaces C^m into complex projective spaces P^n(C) that for any given hypersurface D in P^n(C), f has the prescribed deficient value for D. Mizuhra showed the weak factorization theorem of H^1-functions due to Morrey functions, blocks and the Riesz potential. Also applying this result, we observed the necessity for which the commutator between the Riesz potential and a locally integrable function to be bounded on Morrey Spaces. Nakada studied some geometric properties of the Julia set of rational functions on the Riemann sphere. In particular, it is concerned with the group of euclidean motions which keep invariant the Julia set. Kawamura discussed an generalization of the theory concerning the behavior of probability density functions associated with chaotic maps on a measure space. The spaces he considered were AL and AM spaces and he generalized a convergence theory of probability density functions. Sekigawa examined some examples of transformations with torsion acting on the 3-dimensional Euclidean space by using Clifford matrix representations of M\" obius transformation.
|
