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Generalized Hankel operators on the Fock space II

✍ Scribed by Georg Schneider; Kristan Schneider

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
178 KB
Volume
284
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

In this paper we study boundedness of generalized Hankel operators of the form \documentclass{article}\usepackage{amssymb,mathrsfs}\begin{document}\pagestyle{empty}${\rm H}_{{\overline{z}}^k}^l: {\mathscr F}^2\big (|z|^2\big )\rightarrow L^2\big (|z|^2\big )$\end{document} and thereby extend our results from 10. Here, \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\rm H_{{\overline{z}}^k}^l(f):=(\rm Id-\rm P_l)\big (\overline{z}^k f\big )$\end{document} and P~l~ is the projection onto \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$A^2_l\big (\mathbb C,| z|^2\big ):=\rm cl\big (\rm span\lbrace \overline{z} ^mz^n,|,m,n\in \mathbb N,,m\le l\rbrace \big )$\end{document}. Additionally, we extend our results to general conjugate‐holomorphic L^2^ symbols. The arguments applied show a tight connection between operator theory and combinatorics.

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