一般超幾何.微分方程式の解空間の構造とその積分幾何学的側面

一般超几何。微分方程解空间的结构及其积分几何方面

• 批准号: 07210211
• 负责人: 筧 知之
• 金额: $ 1.09万
• 依托单位: University of Tsukuba
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research on Priority Areas
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 无数据
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-07210211/
• 关键词: 超幾何型微分作用素; ラドン変換; 反転公式; 不変微分作用素; グラスマン多様体

一般超幾何型微分方程式は、多変数特殊関数の理論,ツイスター理論,等、様々な分野で現われ、重要な役割を果たしている。そして、この方程式を重要たらしめている理由の1つが一般超幾何型微分方程式の解空間がある種の多様体のRadon変換の像として表わされる、という事実である。本研究では、最も重要な対象の1つであるグラスマン多様体の上の超幾何型微分方程式を扱い、次の結果を得た.(1)rankrの複素グラスマン多様体上には、(r-1)個の超幾何型不変微分作用素が存在し、各次数は2j(2≦j≦r)である。次数2jのものをΦ_jと表わす事にする。すると超幾何型微分方程式Φ_su=0(2≦s≦r)の解空間KerΦ_sは、rank(s-1)の複素グラスマン多様体上のRadon変換R^r_Sの像として表わされる.即ち“ImRs=KerΦs"(R^r_Sは、rank(S-1)のグラスマン多様体から、rankrのグラスマン多様体へのRadon変換である)そして、上記の超幾何型微分作用素Φsの具体的な表示を得た。(2)上記のrange theoremの応用として、Φsのradial partの具体的な表示、及び各既約な固有空間上でのΦsの固有値の具体的な表示を得た。ラプラシアンΔ及びΦs(2≦s≦r)がrankrのグラスマン多様体上の不変微分作用素のつくる代数の生成元を与えていることを考慮すると、これらの結果は、グラスマン多様体上の不変微分作用素の積分幾何学的特徴付けを与えている。ranksからrankrのグラスマン多様体へのRadon変換の反転公式の具体的な形を得た。これはGrinbergの結果を大幅に改良するものである

General super differential equations, multivariate special differential equations, multivariate special differential equations, general differential equations, multivariate special differential equations, general differential equations, multivariate special differential equations, general differential equations, multivariate special differential equations, general differential equations, multivariate special differential equations, general differential equations, multivariate special differential equations, general differential equations, multivariate special differential equations, general differential equations, multivariate special differential equations, multivariate special differential equations The equation is very important. The equation is very important. In general, the differential equation can be used to solve the space equation. The Radon equation is similar to the table table. In this study, the most important results are as follows: (1) there are two kinds of differential equations in the multibody of rankr complex, (1) there are two kinds of differential factors in each number of times, (1) there are two kinds of differential differential equations in the multibody, and the results of the sub-equation are obtained. (1) the number of times is 2j (2j). The number of times is 2j, the number of times is Φ _ j, the number of times is 2j. The differential equation Φ _ su=0 (2s) is used to solve the spatial Ker Φ _ s equation and rank (Smurl) complex equation. The Radon equation R _ S is similar to that of the spatial differential equation Φ _ r (2cm). That is to say, the "ImRs= kernels" (R ^ r _ S, rank (Smur1) differential interaction factor Φ s) are specifically expressed in terms of "R ^ r _ S", "rankr", "Radon", and "super". (2) the upper range theorem is denoted by the license, the Φ s radial part, and the inherent space of each contract is expressed by the Φ s inherent space. In terms of the number of differential agents, the generator of algebra, the generator of differential agents, the generators of algebra, the generators of differential agents, the generators of algebra, the generators of differential agents, the generators of algebra, the generators of differential agents, the generators of algebra, the generators of differential agents, the generators of algebra, the generators of differential agents, the generators of algebra, the generators of differential agents, the generators of algebra, the generators of algebra, the generators of differential agents, the generators of algebra, algebra and algebra. Ranks, rankr, multiple bodies, Radon, inverse formula, the specific shape. The results of the Grinberg results have been greatly improved.

项目成果

T.KAKEHI: "Range characterization of Radon transforms on quaternionic projective spaces" Mathematische Annalen. 301. 613-625 (1995)

T.KAKEHI：“四元射影空间上氡变换的范围表征”数学年鉴。

T. KAKEHI: "Eigenfunction Expansion associated with the Cusimir operator on the quantum group SUg (1.1)" Duke Mathematical Journal. 80. 535-573 (1995)

T. KAKEHI：“与量子群 SUg (1.1) 上 Cusimir 算子相关的本征函数展开式”杜克数学杂志。

T.KAKEHI: "Spectral analysis of a q-difference operator which arises from the quantum SU (1.1) group" Journal of Operator Theory. 33. 159-196 (1995)

T.KAKEHI：“来自量子 SU (1.1) 群的 q 差算子的谱分析”算子理论杂志。

T. KAKEHI: "Logarithmic divergence of heat kernels on some quantum spaces" Tohoku Mathematical Journal. 47. 595-600 (1995)

T. KAKEHI：“某些量子空间上热核的对数散度”东北数学杂志。