Bøger af Lars Hormander

Grundlehren Der Mathematischen Wissenschaften In Einzeldarstellungen Mit Besonderer Berucksichtigung Der Anwendungsgebiete, V116.

Denna bok är en nyutgåva av ett kompendium om analytiska funktioner i en komplex variabel som Lars Hörmander gav 1979.

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.

Two chapters concern the existence of global solutions or estimates of the lifespan for solutions of nonlinear perturbations of the wave or Klein-Gordon equation with small initial data.

Author received the 1962 Fields MedalAuthor received the 1988 Wolf Prize (honoring achievemnets of a lifetime)Author is leading expert in partial differential equations