| Project/Area Number |
11640181
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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 | International Christian University |
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Principal Investigator |
MORIMOTO Mitsuo College of Liberal Arts, Professor, 教養学部, 教授 (80053677)
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| Co-Investigator(Kenkyū-buntansha) |
GRANT Pogosyan College of Liberal Arts, Professor, 教養学部, 教授 (90234640)
SUZUKI Hiroshi College of Liberal Arts, Professor, 教養学部, 教授 (10135767)
YAMAKAWA Aiko College of Liberal Arts, Assistant Professor, 教養学部, 助教授 (80112754)
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| Project Period (FY) |
1999 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2001: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2000: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1999: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | Complex sphere / Analytic functional / Harmonic function / Entire function of exponential type / Fourier-Borel transformation / Reproducing kernel / Lie ball / Dual Lie ball / フーリェ・ボレル変換 |
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| Research Abstract |
In connection with that analytic functions and analytic functionals on the compex sphere are as boundary values of holomorphic harmonic functions in the Lie ball, we treat in [1] an integral rep-resention of Cauchy-Hua type. The entire functions which are the Fourier-Borel image of analytic functionals on the complex sphere are eigenfunctions of the Laplacian operator. In [2] we represent these eigenfunctions as an integral over the complex light cone. In [3] we treat the Fourier transfor-mation on the Hardy space of harmonic functions on the Lie ball
In [5] we study the reproducing kernel related with the complex sphere. In the papers [6] and [7] we discuss the relation between generalized functions, e.g., distributions, hyperfunctions, on the (real) sphere and solutions of the heat conduction equation. In [6] we study the one dimensional case, while in [7] we consider the n-dimensional sphere. These studies rely on the head investigator's results on the sphererical harmonic expansion of generalized functions on the real sphere. In [8] we study the double series expansion of holomorphic functions on the Lie ball, the dual Lie ball, or the complex Euclidean ball. [12] is a survey paper on the double series expansion. The last paper [13] shows there are a series of norms on the complex Euclidean space including the Lie norm, the dual Lie norm and the Euclidean norm. The result is given with calculation
In [11] we study how to define the Boehrnians on the sphere. The Boehmian is a generalized function usually defined on the Euclidean space by means of convolution. The convolution on the Euclidean space is a commutative operation but the convolution on the rotation group is not. We show two methods to overcome this difficulty
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