Modern Birkhäuser Classics

Notions of Convexity

Authors: Hörmander, Lars

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About this book

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.

Table of contents (7 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-0-8176-4585-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-0-8176-4584-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Notions of Convexity
Authors
Series Title
Modern Birkhäuser Classics
Copyright
1994
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4585-4
DOI
10.1007/978-0-8176-4585-4
Softcover ISBN
978-0-8176-4584-7
Series ISSN
2197-1803
Edition Number
1
Number of Pages
VIII, 416
Additional Information
Originally published as volume 127 in the series: Progress in Mathematics
Topics