We investigate positive definiteness of the Brownian kernel K(x,y) = 1/2(d(x,x₀) + d(y,x₀) - d(x,y)) on a compact group G and in particular for G = SO(n).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-2-9, author = {Paolo Baldi and Maurizia Rossi}, title = {On L\'evy's Brownian motion indexed by elements of compact groups}, journal = {Colloquium Mathematicae}, volume = {131}, year = {2013}, pages = {227-236}, zbl = {1292.43005}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-2-9} }
Paolo Baldi; Maurizia Rossi. On Lévy's Brownian motion indexed by elements of compact groups. Colloquium Mathematicae, Tome 131 (2013) pp. 227-236. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm133-2-9/