Higher order Hilbert-Schmidt Hankel forms and tensors of analytical kernels
The symbols of n^th -order Hankel forms defined on the product of certain reproducing kernel Hilbert spaces H(k_i), i=1,2, in the Hilbert-Schmidt class are shown to coincide with the orthogonal complement in H(k_1)H(k_2) of the ideal of polynomials which vanish up to order n along the diagonal. For tensor products of weighted Bergman and Dirichlet type spaces (including the Hardy space) we introduce a higher order restriction map which allows us to identify the relative quotient of the n^th -order ideal modulo the (n+1)^st -order one as a direct sum of single variable Bergman and Dirichlet-type spaces. This generalizes the well understood 0^th -order case., number=1, journal=MATHEMATICA SCANDINAVICA, author=Ferguson, Sarah H. and Rochberg, Richard, year=2005, month=Mar., pages=117–146