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RT Book, Whole SR Electronic DC OPAC T1 Notions of Convexity / by Lars Hörmander T2 Modern Birkhäuser Classics A1 Hörmander, Lars A1 SpringerLink (Online service) YR 1994 FD 1994 SP VIII, 416 p K1 Mathematics K1 Mathematical analysis K1 Analysis (Mathematics) K1 Partial differential equations K1 Potential theory (Mathematics) K1 Functions of real variables K1 Functions of complex variables K1 Convex geometry K1 Discrete geometry K1 Mathematics K1 Several Complex Variables and Analytic Spaces K1 Convex and Discrete Geometry K1 Real Functions K1 Potential Theory K1 Analysis K1 Partial Differential Equations PB Birkhäuser Boston PP Boston, MA SN 9780817645854 LA English (英語) CL DC23:515.94 NO 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 NO 書誌ID=1002989337; LK [E Book]http://dx.doi.org/10.1007/978-0-8176-4585-4 OL 30