Singular Fourier Integral Operators, Micro-hyperbolicity and second microlocalization

奇异傅立叶积分算子、微双曲性和二次微定位

• 批准号: 15540185
• 负责人: TOSE Nobuyuki
• 金额: $ 2.24万
• 依托单位: Keio University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540185/
• 关键词: microlocal analysis; Fourier integral operators; micro-hyperbolicity; second microlocalization; conical refraction; microfunction; hyperfunctions; crystal optics; conical refraction; 多曲型方程式; 積分幾何; 特異積分作用素; 変換理論; 双曲型方程式; 作用素の標準形; 標準形; 代数解析

In the study of propagation of (microlocal) singularities of solutions to linear hyperbolic equations, a variety of phenomenon such as branching of singularities and conical refraction. In particular, conical refraction has been studied from many points of vies since it appeared naturally in natural world. Around 1885, in the study of conical refraction, the method of second microlocalization was employed, which blow-up the phase space along an involutive submanifold. This made it possible to obtain a certain successful result by P. Laubin and N. Tose. But there still remained some problems as far as existence of solutions is concerned. In this research, a transformation theory for operators in the category of second microlocalization is constructed.

在研究线性双曲型方程解的（微局部）奇性传播时，经常会遇到奇性分支和锥折射等现象。特别是圆锥折射，自从它在自然界中自然出现以来，人们从多个角度对其进行了研究。1885年前后，在研究圆锥折射时，采用了二次微局部化方法，即沿沿着对合子流形将相空间爆破。这使得P.Laubin和N.东濑但就解决方案的存在而言，仍存在一些问题。在这项研究中，在第二微局部化范畴内的算子的转换理论的建设。

项目成果

Second Microlocalization, Regular Sequences, and Fourier Inverse Transforms

第二微定位、正则序列和傅里叶逆变换

• 发表时间: 2005
• 期刊: 数理解析研究所講究録 1412
• 作者: O.Liess;Y.Okada;N.Tose
• 通讯作者: N.Tose

経済数学

经济数学

• 发表时间: 2005
• 作者: S.Mecheri;K.Tanahashi;A.Uchiyama;戸瀬信之
• 通讯作者: 戸瀬信之

Microlocalization, Regular Sequences and Fourier Transforms

微定位、正则序列和傅里叶变换

• 发表时间: 2005
• 期刊: 京都大学数理解析研究所講究録 1412
• 作者: Liess;OTTO;岡田靖則;戸瀬信之
• 通讯作者: 戸瀬信之