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

Authors

  • Sarah H. Ferguson
  • Richard Rochberg

DOI:

https://doi.org/10.7146/math.scand.a-14948

Abstract

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.

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Published

2005-03-01

How to Cite

Ferguson, S. H., & Rochberg, R. (2005). Higher order Hilbert-Schmidt Hankel forms and tensors of analytical kernels. MATHEMATICA SCANDINAVICA, 96(1), 117–146. https://doi.org/10.7146/math.scand.a-14948

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Section

Articles