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Notions of Convexity
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Notions of Convexity

Notions of Convexity

Lars Hormander - Collection Progress in Mathematics

414 pages, parution le 01/01/2007 (2eme édition)

Résumé

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.

L'auteur - Lars Hormander

Born on January 24,1931, on the southern coast of Sweden, Lars Hormander did his secondary schooling as well as his undergraduate and doctoral studies in Lund. His principle teacher and adviser at the University of Lund was Marcel Riesz until he returned, then Lars Carding. In 1956 he worked in the USA, at the universities of Chicago, Kansas, Minnesota and New York, before returning to a chair at the University of Stockholm. He remained a frequent visitor to the US, particularly to Stanford and was Professor at the IAS, Princeton from 1964 to 1968. In 1968 he accepted a chair at the University of Lund, Sweden, where, today he is Emeritus Professor.

Hormander's lifetime work has been devoted to the study of partial differential equations and its applications in complex analysis. In 1962 he was awarded the Fields Medal for his contributions to the general theory of linear partial differential operators. His book Linear Partial Differential Operators, published 1963 by Springer in the Grundlehren series, was the first major account of this theory. His four volume text The Analysis of Linear Partial Differential Operators, published in the same series 20 years later, illustrates the vast expansion of the subject in that period.

Sommaire

  • Convex 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
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  PAPIER
Éditeur(s) Birkhäuser
Auteur(s) Lars Hormander
Collection Progress in Mathematics
Parution 01/01/2007
Édition  2eme édition
Nb. de pages 414
Format 15,5 x 23,5
Couverture Broché
Poids 545g
Intérieur Noir et Blanc
EAN13 9780817645847
ISBN13 978-0-8176-4584-7

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