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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Locally Convex Spaces and Linear Partial Differential Equations

Locally Convex Spaces and Linear Partial Differential Equations

Treves, François

Paperback

Series: Grundlehren Der Mathematischen Wissenschaften, Book 146

CalculusGeneral Mathematics

ISBN10: 3642873731
ISBN13: 9783642873737
Publisher: Springer Nature
Published: Apr 21 2012
Pages: 123
Weight: 0.45
Height: 0.30 Width: 6.14 Depth: 9.21
Language: English
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.

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