Lars Hörmander

Notions of Convexity

• Broschiertes Buch

Produktbeschreibung

The term convexity used to describe these lectures given at the Univer sity of Lund in 1991-92 should be understood in a wide sense. Only Chap ters I and II are devoted to convex sets and functions in the traditional sense of convexity. The following chapters study other kinds of convexity which occur in analysis. Most prominent is the pseudo-convexity (plurisubh- monicity) in the theory of functions of several complex variables discussed in Chapter IV. It relies on the theory of subharmonic functions in R^, so Chapter III is devoted to subharmonic functions in R"^ for any n. Existence theorems for constant coefficient partial differential operators in R'^ are re lated to various kinds of convexity conditions, depending on the operator. Chapter VI gives a survey of the rather incomplete results which are known on their geometrical meaning. There are also natural classes of "convex" functions related to subgroups of the linear group, which specialize to sev eral of the notions already mentioned. They are discussed in Chapter V. The last chapter. Chapter VII, is devoted to the conditions for solvability of microdifferential equations, which can also be considered as a branch of convexity theory. The whole chapter is an exposition of a part of the thesis of J.-M. Trepreau.

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Produktdetails

• Modern Birkhäuser Classics
• Verlag: Birkhäuser / Birkhäuser Boston / Springer, Basel
• Artikelnr. des Verlages: 11940395, 978-0-8176-4584-7
• Repr. of the 1994 ed.
• Seitenzahl: 414
• Erscheinungstermin: 27. Dezember 2006
• Englisch
• Abmessung: 236mm x 156mm x 27mm
• Gewicht: 673g
• ISBN-13: 9780817645847
• ISBN-10: 0817645845
• Artikelnr.: 21359444

Autorenporträt

Lars Hörmander, born 1931 in Sweden, 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 Gårding. 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.

Hörmander'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.

Inhaltsangabe

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 (.?).