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We present decompositions of various positive kernels as integrals or sums of positive kernels. Within this framework we study the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions. As a tool, we define a new function of two complex variables, which is a natural generalization of the classical Gamma function for the setting we consider.


This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Potential Analysis, volume 28, in 2008 following peer review. The final publication is available at Springer via DOI: 10.1007/s11118-007-9070-4

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