Study of global solutions to Fuchsian equations and local solutions to linear PDE

Fuchsian方程全局解和线性偏微分方程局部解的研究

基本信息

  • 批准号:
    15540156
  • 负责人:
  • 金额:
    $ 1.86万
  • 依托单位:
  • 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 2005
  • 项目状态:
    已结题

项目摘要

1.We tried second microlocal analysis for some class of Turrittin equations with lower terms of homogeneous type. In this case, similarly to the case of Mizohata equations, it became clear that fundamental solutions can be constructed using the theory of second microlocal Fourier transformations. Here we used the result about the growth order for the global solutions to some ordinary differential equations in the space where Fourier transforms live. In more special cases, the inverse Fourier transform satisfies some Fuchsian equations. We got the information of the Fuchsian equations, singularities, exponents, and some behaviors of their solutions.2.On the other hand, we can consider the notion of microfunctions with holomorphic parameters on a product space of a real domain and a complex domain. They are represented as boundary values of holomorphic functions, and their boundary values define the notion of second microfunctions, and so on. The equations in 1 have microlocal ellipticity in rather small region, but we can construct their second microlocal solutions by the actions of their inverses to microfunctions with holomorphic parameters. The relation between this result and the theory of boundary values of pseudo-differential operators due to Kataoka will be a further subject.3.A fundamental solution to linear PDE can be regarded as a kernel function of an integral transformation. We studied the kernels under an expectation that an integral transformation with kernel should be characterized by some notion similar to continuity, and got the kernel theorems in analytic category, by introducing notion of semi-continuity. Here we used the construction of complex kernels with curvilinear Radon transformations.
1.对几类齐次型低项Turrittin方程进行了第二次微局部分析。在这种情况下,类似于Mizohata方程的情况,很明显,基本解可以使用第二微局部傅里叶变换理论来构造。在这里,我们使用的结果的增长阶的一些常微分方程的整体解的空间中的傅立叶变换。在更特殊的情况下,逆傅里叶变换满足一些Fuchsian方程。我们得到了Fuchsian方程的解、奇性、指数以及解的一些性质。2.另一方面,我们可以考虑在一个真实的区域和一个复区域的乘积空间上具有全纯参数的微函数的概念。它们被表示为全纯函数的边值,而它们的边值定义了第二微函数的概念,等等,文[1]中的方程在很小的区域内具有微局部椭圆性,但我们可以通过它们的逆函数对具有全纯参数的微函数的作用来构造它们的第二微局部解。这一结果与Kataoka的伪微分算子边值理论之间的关系将是进一步的研究课题。3.线性偏微分方程的基本解可以看作是积分变换的核函数。我们在一个期望下研究了核,即一个具有核的积分变换应该用类似于连续性的概念来刻画,并通过引入半连续性的概念,得到了解析范畴中的核定理。在这里,我们使用了曲线Radon变换的复杂核的构造。

项目成果

期刊论文数量(41)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Second Microlocalization, Regular Sequences, and Fourier Inverse Transforms
第二微定位、正则序列和傅里叶逆变换
Numerical radius norm for bounded module maps and Schur multipliers
有界模块映射和 Schur 乘数的数值半径范数
Transformations de Fourier-Sato et ope 'rateurs pseudo-diffe' rentiels non-locaux
傅立叶-佐藤变换和非本地“伪差异”租金操作者的变换
Stability properties of Linear Volterra integrodiffenrential equations in a Banach space
Banach 空间中线性 Volterra 积分微分方程的稳定性性质
  • DOI:
  • 发表时间:
    2005
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Y.Hino;S.Murakami
  • 通讯作者:
    S.Murakami
Transformations de Fourier-Sato et ope' rateurs pseudo-diffe' rentiels non-locaux
傅里叶-佐藤变换和非本地的伪不同的租金变换
  • DOI:
  • 发表时间:
  • 期刊:
  • 影响因子:
    0
  • 作者:
    H.Shiga;T.Tsutsui;J.Wolfart;R.Ishimura;R.Ishimura
  • 通讯作者:
    R.Ishimura
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OKADA Yasunori其他文献

OKADA Yasunori的其他文献

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{{ truncateString('OKADA Yasunori', 18)}}的其他基金

Pathological study on metalloproteinases in tissue remodeling under pathological conditions
病理条件下金属蛋白酶参与组织重塑的病理学研究
  • 批准号:
    24249022
  • 财政年份:
    2012
  • 资助金额:
    $ 1.86万
  • 项目类别:
    Grant-in-Aid for Scientific Research (A)
Study of integral transformations in hyperfunctions and differential operators of infinite order
超函数积分变换和无限阶微分算子的研究
  • 批准号:
    22540173
  • 财政年份:
    2010
  • 资助金额:
    $ 1.86万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Functional analyses and regulation of the metabolism of tissue microenvironmental factors by metalloproteinases
金属蛋白酶对组织微环境因子代谢的功能分析和调节
  • 批准号:
    19109004
  • 财政年份:
    2007
  • 资助金额:
    $ 1.86万
  • 项目类别:
    Grant-in-Aid for Scientific Research (S)
Pathological studies on the tissue destruction by metalloproteinases
金属蛋白酶组织破坏的病理学研究
  • 批准号:
    16209015
  • 财政年份:
    2004
  • 资助金额:
    $ 1.86万
  • 项目类别:
    Grant-in-Aid for Scientific Research (A)
Research concerning Privacy Protection Principles about Data Transfer from EU to the United States
欧盟至美国数据传输隐私保护原则研究
  • 批准号:
    14520022
  • 财政年份:
    2002
  • 资助金额:
    $ 1.86万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Regulation of MT1-MMP gene expression by HMGI-C
HMGI-C对MT1-MMP基因表达的调控
  • 批准号:
    11694311
  • 财政年份:
    1999
  • 资助金额:
    $ 1.86万
  • 项目类别:
    Grant-in-Aid for Scientific Research (A)
Molecular Pathology of Cartilage destruction in Rheumatoid Arthritis
类风湿关节炎软骨破坏的分子病理学
  • 批准号:
    10470051
  • 财政年份:
    1998
  • 资助金额:
    $ 1.86万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Analyzes on ECM metabolism in transgenic and knockout mice
转基因和基因敲除小鼠 ECM 代谢分析
  • 批准号:
    08044262
  • 财政年份:
    1996
  • 资助金额:
    $ 1.86万
  • 项目类别:
    Grant-in-Aid for international Scientific Research
Studies on the destruction of articular cartilage by matrix metalloproteinases
基质金属蛋白酶破坏关节软骨的研究
  • 批准号:
    07457049
  • 财政年份:
    1995
  • 资助金额:
    $ 1.86万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)

相似海外基金

Study on half-space problem for non-linear PDE in Fluid Dynamics and its application
流体动力学非线性偏微分方程半空间问题研究及其应用
  • 批准号:
    21740105
  • 财政年份:
    2009
  • 资助金额:
    $ 1.86万
  • 项目类别:
    Grant-in-Aid for Young Scientists (B)
Study on stationary solution to non-linear PDE in Fluid Dynamics
流体动力学中非线性偏微分方程平稳解的研究
  • 批准号:
    18740081
  • 财政年份:
    2006
  • 资助金额:
    $ 1.86万
  • 项目类别:
    Grant-in-Aid for Young Scientists (B)
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