【超级大牛巨献】
凸分析

Notions of Convexity  by Lars Hormander
English | 2007| ISBN: 0817637990 | Pages: 414 | PDF | 14 MB
【作者简介】
Lars Valter Hormander（1931年1月24日－2012年11月25日），瑞典数学家，涉及的研究领域很广，尤其在现代线性偏微分方程现代理论做出了巨大贡献。他于1962年荣获菲尔兹奖，1988年荣获沃尔夫奖，他的Analysis of Linear Partial Differential Operators I - IV（《线性偏微分算子分析》）被认为是线性偏微分算子领域的最经典文献。他于1955年在隆德大学获得博士学位，1968年起任该校教授，直至1996年退休，其间他曾经在斯坦福大学、普林斯顿大学等高校任教，1987—1990年间，他曾任国际数学联盟副主席。

【教材简介】
The first two chapters of this book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in the following chapters of related notions which occur in the theory of linear partial differential equations and complex analysis such as (pluri-)subharmonic functions, pseudoconvex sets, and sets which are convex for supports or singular supports with respect to a differential operator.

In addition, the convexity conditions which are relevant for local or global existence of holomorphic differential equations are discussed, leading up to Trépreau’s theorem on sufficiency of condition (capital Greek letter Psi) for microlocal solvability in the analytic category.

At the beginning of the book, no prerequisites are assumed beyond calculus and linear algebra. Later on, basic facts from distribution theory and functional analysis are needed. In a few places, a more extensive background in differential geometry or pseudodifferential calculus is required, but these sections can be bypassed with no loss of continuity. The major part of the book should therefore be accessible to graduate students so that it can serve as an introduction to complex analysis in one and several variables. The last sections, however, are written mainly for readers familiar with microlocal analysis.
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