عنوان

Locally Convex Spaces and Linear Partial Differential Equations

(Number (ISBN

3642873715

(Number (ISBN

3642873731

(Number (ISBN

9783642873713

(Number (ISBN

9783642873737

Number

b574842

Title Proper

Locally Convex Spaces and Linear Partial Differential Equations

General Material Designation

[Book]

First Statement of Responsibility

by François Treves.

Place of Publication, Distribution, etc.

Berlin, Heidelberg

Name of Publisher, Distributor, etc.

Springer Berlin Heidelberg

Date of Publication, Distribution, etc.

1967

Series Title

Die Grundlehren der mathematischen Wissenschaften, In Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, 146.

Text of Note

I. The Spectrum of a Locally Convex Space --; I. The Spectrum of a Locally Convex Space --; II. The Natural Fibration over the Spectrum --; III. Epimorphisms of Fréchet Spaces --; IV. Existence and Approximation of Solutions to a Functional Equation --; V. Translation into Duality --; II. Applications to Linear Partial Differential Equations --; VI. Applications of the Epimorphism Theorem --; VII. Applications of the Epimorphism Theorem to Partial Differential Equations with Constant Coefficients --; VIII. Existence and Approximation of Solutions to a Linear Partial Differential Equation --; IX. Existence and Approximation of Solutions to a Linear Partial Differential Equation --; Appendix A: Two Lemmas about Fréchet Spaces --; Appendix B: Normal Hilbert Spaces of Distributions --; Appendix C: On the Nonexistence of Continuous Right Inverses --; Main Definitions and Results Concerning the Spectrum of a Locally Convex Space --; Some Definitions in PDE Theory --; Bibliographical References.

Text of Note

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.

Mathematics.

Class number

Book number

by François Treves.

François Treves

Electronic name

[Book]

Y