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Polynomial extensions of compatible polynomial traces in three dimensions

✍ Scribed by Faker Ben Belgacem

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
365 KB
Volume
116
Category
Article
ISSN
0045-7825

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✦ Synopsis

We describe the construction of polynomial extension operators of polynomial traces over the reference cube satisfying optimal stability conditions with respect to Sobolev norms. Combined with Hilbertian interpolation argument, these results show the equivalence of Sobolev norms and the interpolation norms on spaces of polynomials defined over a square.

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As an example, consider the elliptic curve E: y 2 +xy=x 3 +:, where : generates GF(4), the field with four elements, and take l to be 5. There are 25 elements of E[5], including the identity element and twelve pairs P i =(x i , y i ) and &P i =(x i , x i + y i ). The twelve distinct x-coordinates ar