We systematically discuss the consequences of genuine dimension-six Higgs
operators. These operators are not subject to stringent constraints from
electroweak precision data. However, they can modify the couplings of the Higgs
boson to electroweak gauge bosons and, in particular, the Higgs
self-interactions. We study the sensitivity to which those couplings can be
probed at future \ee linear colliders in the sub-TeV and in the multi-TeV
range. We find that for s=500 GeV with a luminosity of 1 ab−1 the
anomalous WWH and ZZH couplings may be probed to about the 0.01 level, and
the anomalous HHH coupling to about the 0.1 level.Comment: 21 pages, 17 figures; typos corrected and references adde