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MARC 21

Notions of Convexity
Tag	Description
020	$a9780817645854
082	$a515.94
099	$aOnline Resource: Birkhäuser
100	$aHörmander, Lars
245	$aNotions of Convexity
245	$h[EBook]$cby Lars Hörmander.
250	$aReprint of the 1994 edition
260	$aBoston, MA$bBirkhäuser$c2007
300	$aVIII, 416 pages$bonline resource.
336	$atext
338	$aonline resource
440	$aModern Birkhäuser Classics
505	$aConvex Functions of One Variable -- Convexity in a Finite-Dimensional Vector Space -- Subharmonic Functions -- Plurisubharmonic Functions -- Convexity with Respect to a Linear Group -- Convexity with Respect to Differential Operators -- Convexity and Condition (.?).
520	$aConvex Functions of One Variable.- Convexity in a Finite-Dimensional Vector Space.- Subharmonic Functions.- Plurisubharmonic Functions.- Convexity with Respect to a Linear Group.- Convexity with Respect to Differential Operators.- Convexity and Condition (.?).$aThe 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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
710	$aSpringerLink (Online service)
830	$aModern Birkhäuser Classics
856	$uhttp://dx.doi.org/10.1007/978-0-8176-4585-4