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arxiv: math/0410491 · v1 · submitted 2004-10-22 · 🧮 math.FA · math.CO

Tensor algebras and displacement structure. IV. Invariant kernels

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keywords displacementinvariantkernelkernelsalgebrasclasscombinatorialdefinite
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In this paper we investigate the class of invariant positive definite kernels on the free semigroup on N generators. We provide a combinatorial description of the positivity of the kernel in terms of Dyck paths and then we find a displacement equation that encodes the invariance property of the kernel.

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