強擬凸領域における再生核の族の漸近解析

强赝凸区域中一族再生核的渐近分析

• 批准号: 05640181
• 负责人: 小松 玄
• 金额: $ 1.28万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1993
• 资助国家: 日本
• 起止时间: 1993 至 无数据
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-05640181/
• 关键词: ベルグマン核; ゼゲー核; 複素モンジュ-アンペール境界値問題; CR不変量; ワイル不変量; 強擬凸領域; モーザーの漂準形; 普遍定数

滑らかな境界を持つ強擬凸領域においてベルグマン核と双正則不変なゼゲー核を考える.それらを領域の対角集合に制限したものは,共に境界上に超幾何函数の形の特異性を持つ.即ち,領域の定義函数を一つ指定すると,それに関して負べきの形の強い特異性と対数の形の弱い特異性の和になっている.これらの特異性の係数となる函数から領域の境界の幾何学的な量を局所双正則不変な形に取り出そうというのが,フェッファーマンの目録である.領域が複素二次元の場合には,従来の研究によって,ウェイトが4以下の局所不変量が普遍定数の決定を込めて完全な形で取り出されている.ウェイトが5以下の局所不変量を取り出せなかった主な理由は,ウェイトが4のCR不変量を領域内部に近似的に局所双正則不変な形に拡張する仕方がわからなかったことである.当研究において,複素二次元領域の場合に,ウェイトが4のCR不変量がワイル不変量であることがわかった.このことを使うと,ベルグマン核と不変なゼゲー核に含まれるウェイトが5以下の局所不変量を,普遍定数の決定を除いて,取り出すことができる.普遍定数を決定するためには,ベルグマン核・不変なゼゲー核・複素モンジュ-アンペール境界値問題の解・ワイル不変量の各々の漸近展開を,モーザーの標準形の係数を用いて必要なところまで書き表わせばよい.当研究においては,そのことも実行した.こうして,滑らかな境界を持つ複素二次元の強擬凸領域において,ベルグマン核と双正則不変なゼゲー核に含まれるウェイトが5以下の局所双正則不変量を,普遍定数の決定を込めて完全な形で取り出すことができた.

A sliding boundary is a strongly quasi-convex domain, and a biregular kernel is a biregular kernel. The set of angles in the domain is restricted to the form of hypergeometric functions in the domain. That is, the definition function of the domain specifies that the domain has a strong specificity and a weak specificity. The coefficient of specificity of the function is the geometric quantity of the boundary of the field. In the case of complex prime quadratic dimension, it is necessary to study the future, and it is necessary to determine the general fixed number of variables below 4. For example, if you want to find out the main reason, you can find out the reason why you want to find out the main reason. If you want to find out the reason why you want to find out the main reason, you can find out the reason why you want to find out the main reason. If you want to find out the main reason, you can find out the reason why you want to find out the main reason. If you want to find out the main reason, you can find out the reason why you want to find out the main reason. If you want to find out the reason why you want to find out the main reason, you can find out the reason why you want to find out the main reason. If you want to find out the reason why you want to find the main reason, you can find the reason why you want to find the main reason. If you want to find out the main reason, you want to find out the reason why you want to find the main reason. If you want to find out the main reason, you want to find out the reason why you want to find the main reason. If you want to find out the main reason, you want to find the reason why you When we study the complex quadratic domain, we find that it has 4 CR values and 4 CR values. This is the first time that a decision has been made on a fixed number. The general fixed number is determined by the asymptotic expansion of the boundary value problem, the coefficient of the standard form of the boundary value problem, and the necessary coefficient of the standard form. When the study is done, it is done. The boundary of a complex element is a strongly quasi-convex domain. The boundary of a complex element is a strongly quasi-convex domain. The boundary of a complex element is a strongly quasi-convex domain. The boundary of a complex element is a strongly quasi-convex domain.

项目成果

Atsusi Kasue: "Measured Hausdorff convergence of Riemannian manifolds and Laplace operators" Osaka J.Math.30. 613-651 (1993)

Atssi Kasue：“黎曼流形和拉普拉斯算子的测量豪斯多夫收敛性”Osaka J.Math.30。

Atsusi Kasue: "Spectral convergence of Riemannian manifolds" to appear in Tohoku Math.J.36

Atsusi Kasue：“黎曼流形的谱收敛”出现在东北数学.J.36

Kengo Hirachi: "The second variation of the Bergman kernel of ellipsoids" Osaka J.Math.30. 457-473 (1993)

Kengo Hirachi：“椭球伯格曼核的第二个变体”Osaka J.Math.30。

Kengo Hirachi: "Scalar pseudo-hermitian invariants and the Szego kernel on three-dimensional CR manifolds" Lecture Notes in Pure Appl.Math.,Marcel Dekker. 143. 67-76 (1993)

Kengo Hirachi：“三维 CR 流形上的标量伪厄米不变量和 Szego 核”纯应用数学讲义，Marcel Dekker。

Gen Komatsu(editor): "Complex Geometry Lecture Notes in Pure and Applied Mathematics,volume 143" Marcel Dekker, 229 (1993)

小松元（编辑）：《纯粹与应用数学中的复杂几何讲义，第 143 卷》Marcel Dekker，229 (1993)