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Sur une equation fonctionnelle

✍ Scribed by Denis Serre


Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
246 KB
Volume
6
Category
Article
ISSN
0893-9659

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✦ Synopsis


We consider the functional equation fi(r) = cj aijf(qr) + hi(z) where oij and rj are fixed constants, 0 < rj < 1, and hi is a given function. The independant real variable z runs either on IO, zo[ or on IO, +a~[. We give necessary and sufficient conditions of algebraic type in order that the linear mapping h ++ f be well-defined and continuous from a Sobolev-type space (one may think to L2($)) into itself. A former analysis within the context of differentiable functions is due to Le Floch and Li Ta Tsien [l].


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