On Certain Group Invariant Mercer Kernels

For the construction of support vector machines Mercer Kernels are of considerable importance. Since the conditions of Mercer’s theorem are hard to verify in general, a systematic (constructive) description of Mercer kernels which are invariant under a transitive group action is provided. As an example kernels on Euclidean space invariant under the Euclidean motion group are treated. En passant a minor but confusing error in a seminal paper due to Gangolli is rectified. In addition an interesting relation to radial basis func-

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