Higher order Hilbert-Schmidt Hankel forms and tensors of analytical kernels
Keyword(s):
The symbols of $n^{\hbox{th}}$-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 $H(k_{1})\otimes H(k_{2})$ 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 $n^{\hbox{th}}$-order ideal modulo the $(n+1)^{\hbox{st}}$-order one as a direct sum of single variable Bergman and Dirichlet-type spaces. This generalizes the well understood $0^{\hbox{th}}$-order case.
2017 ◽
Vol 60
(4)
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pp. 690-704
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2013 ◽
Vol 24
(6)
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pp. 847-861
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Keyword(s):
2021 ◽
Vol 500
(1)
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pp. 125107
2002 ◽
Vol 35
(1)
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pp. 103-108
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2013 ◽
Vol 11
(05)
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pp. 1350020
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2014 ◽
Vol 9
(4)
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pp. 827-931
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2009 ◽
Vol 80
(3)
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pp. 430-453
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