Explicit construction of reproducing kernels
Résumé
In this short Note, we calculate explicitely reproducing kernels for simple Sobolev spaces. In particular, we prove that for each m the reproducing kernel of H m+1 (R 2m) and of H m+1 (R 2m+1) are proportional to the ones of H 2 (R 2) and of H 2 (R 3), the former being characterized by the modified Hankel function K1, the latter by the modified Hankel function K 1 2 .
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