Computing a family of reproducing kernels for statistical applications |
| |
Authors: | Christine Thomas-Agnan |
| |
Institution: | (1) Université des Sciences Sociales, F-31000 Toulouse, France |
| |
Abstract: | For an open subset of , an integer,m, and a positive real parameter , the Sobolev spacesH
m
( ) equipped with the norms: u 2= u(t)2dt+(1/ 2m
u
(m)(t)2 constitute a family of reproducing kernel Hilbert spaces. When is an open interval of the real line, we describe the computation of their reproducing kernels. We derive explicit formulas for these kernels for all values ofm in the case of the whole real line, and form=1 andm=2 in the case of a bounded open interval.This research was partly supported by NSF Grant DMS-9002566. |
| |
Keywords: | Sobolev spaces reproducing kernels Hilbert spaces |
本文献已被 SpringerLink 等数据库收录! |
|