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
• DOI: 10.1016/0893-9659(93)90095-5

✦ 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].