© 1967

Locally Convex Spaces and Linear Partial Differential Equations


Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 146)

Table of contents

  1. Front Matter
    Pages I-XII
  2. The Spectrum of a Locally Convex Space

    1. Front Matter
      Pages 1-1
    2. François Treves
      Pages 3-14
    3. François Treves
      Pages 15-24
    4. François Treves
      Pages 25-36
    5. François Treves
      Pages 43-54
  3. Applications to Linear Partial Differential Equations

  4. Back Matter
    Pages 105-123

About this book


It is hardly an exaggeration to say that, if the study of general topolog­ ical vector spaces is justified at all, it is because of the needs of distribu­ tion and Linear PDE * theories (to which one may add the theory of convolution in spaces of hoi om orphic functions). The theorems based on TVS ** theory are generally of the "foundation" type: they will often be statements of equivalence between, say, the existence - or the approx­ imability -of solutions to an equation Pu = v, and certain more "formal" properties of the differential operator P, for example that P be elliptic or hyperboJic, together with properties of the manifold X on which P is defined. The latter are generally geometric or topological, e. g. that X be P-convex (Definition 20. 1). Also, naturally, suitable conditions will have to be imposed upon the data, the v's, and upon the stock of possible solutions u. The effect of such theorems is to subdivide the study of an equation like Pu = v into two quite different stages. In the first stage, we shall look for the relevant equivalences, and if none is already available in the literature, we shall try to establish them. The second stage will consist of checking if the "formal" or "geometric" conditions are satisfied.


Differential Equations Differential operator Differentialgleichung Lokalkonvexer Raum Manifold Partial Differential Equations Partielle Differentialgleichung differential equation equation function partial differential equation theorem

Authors and affiliations

  1. 1.Purdue UniversityLafayetteUSA

Bibliographic information

  • Book Title Locally Convex Spaces and Linear Partial Differential Equations
  • Authors François Treves
  • Series Title Die Grundlehren der mathematischen Wissenschaften
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1967
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-03833-7
  • Softcover ISBN 978-3-642-87373-7
  • eBook ISBN 978-3-642-87371-3
  • Series ISSN 0072-7830
  • Edition Number 1
  • Number of Pages XII, 123
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
    Partial Differential Equations
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking
IT & Software