Higher order Hilbert-Schmidt Hankel forms and tensors of analytic kernels

Autores: S. H. Ferguson
Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 96, Nº 1, 2005, págs. 117-146
Idioma: inglés
DOI: 10.7146/math.scand.a-14948
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Resumen
- The symbols of nth-order Hankel forms defined on the product of certain reproducing kernel Hilbert spaces H(ki), i=1,2, in the Hilbert-Schmidt class are shown to coincide with the orthogonal complement in H(k1)⊗H(k2) 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 nth-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 0th-order case.