Skip to main content
SpringerLink
Log in

Locally Convex Spaces and Linear Partial Differential Equations

  • Book
  • © 1967

Overview

Authors:
  1. François Treves

    1. Purdue University, Lafayette, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (9 chapters)

  1. Front Matter

    Pages I-XII
    Download chapter PDF

  2. The Spectrum of a Locally Convex Space

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. The Spectrum of a Locally Convex Space

      • François Treves
      Pages 3-14

    3. The Natural Fibration over the Spectrum

      • François Treves
      Pages 15-24

    4. Epimorphisms of Fréchet Spaces

      • François Treves
      Pages 25-36

    5. Existence and Approximation of Solutions to a Functional Equation

      • François Treves
      Pages 37-42

    6. Translation into Duality

      • François Treves
      Pages 43-54

  4. Back Matter

    Pages 105-123
    Download chapter PDF
Back to top

Keywords

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.

Authors and Affiliations

  • Purdue University, Lafayette, USA

    François Treves

Bibliographic Information

  • Book Title: Locally Convex Spaces and Linear Partial Differential Equations

  • Authors: François Treves

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-642-87371-3

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin · Heidelberg 1967

  • Softcover ISBN: 978-3-642-87373-7Published: 21 April 2012

  • eBook ISBN: 978-3-642-87371-3Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: XII, 123

  • Topics: Analysis, Partial Differential Equations

Publish with us

Policies and ethics

Back to top

Search

Navigation