| 期刊全称 | Analytic Partial Differential Equations | | 影响因子2023 | François Treves | | 视频video | | | 发行地址 | A self-contained introduction to the analysis of solutions of partial differential equations on manifolds.Introduces tools of microlocal analysis such as the FBI transform and pseudodifferential opera | | 学科分类 | Grundlehren der mathematischen Wissenschaften | | 图书封面 |  | | 影响因子 | This book provides a coherent, self-contained introduction to central topics of .Analytic Partial Differential Equations. in the natural geometric setting. The main themes are the analysis in phase-space of analytic PDEs and the Fourier–Bros–Iagolnitzer (FBI) transform of distributions and hyperfunctions, with application to existence and regularity questions..The book begins by establishing the fundamental properties of analytic partial differential equations, starting with the Cauchy–Kovalevskaya theorem, before presenting an integrated overview of the approach to hyperfunctions via analytic functionals, first in Euclidean space and, once the geometric background has been laid out, on analytic manifolds. Further topics include the proof of the Lojaciewicz inequality and the division of distributions by analytic functions, a detailed description of the Frobenius and Nagano foliations, and the Hamilton–Jacobi solutions of involutive systems of eikonalequations. The reader then enters the realm of microlocal analysis, through pseudodifferential calculus, introduced at a basic level, followed by Fourier integral operators, including those with complex phase-functions (.à la. Sjöstran | | Pindex | Book 2022 |
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发表于 2025-3-21 19:55:59
