A class of Fourier integral operators with complex phase related to the Gevrey classes

被引：4

作者：

Nishitani, Tatsuo ^{[1
]}

Tamura, Mitsuji ^{[2
]}

机构：

[1] Osaka Univ, Dept Math, Toyonaka, Osaka 5600043, Japan

[2] Tokyo Univ Sci, Fac Sci & Technol, Dept Math, Noda, Chiba 2788510, Japan

来源：

JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS | 2010年 / 1卷 / 03期

关键词：

Cauchy Problem; Phase Function; Analytic Extension; Pseudo Differential Operator; Fourier Integral Operator;

D O I：

10.1007/s11868-010-0014-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we discuss about Fourier integral operators with complex phase functions belonging to S-rho, delta(kappa), 0 < delta < rho <= 1, 0 < kappa < rho - delta where the positivity of imaginary part of the phase functions is not required. In particular we prove composition formulae for 0 and 1 quantization of Fourier integral operators with phase phi and -phi. These results are applied to reduce the Cauchy problem for noneffectively hyperbolic operators in the Gevrey classes to the Cauchy problem in Sobolev spaces.

引用

页码：255 / 292

页数：38

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