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Generalized Hankel operators on the Fock space
Author(s) -
Schneider Georg,
Schneider Kristan A.
Publication year - 2009
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200810169
Subject(s) - mathematics , holomorphic function , fock space , bounded function , generalization , hankel transform , projection (relational algebra) , space (punctuation) , bar (unit) , pure mathematics , section (typography) , operator (biology) , combinatorics , mathematical analysis , algorithm , physics , computer science , quantum mechanics , biochemistry , chemistry , bessel function , repressor , meteorology , transcription factor , gene , operating system
In this paper we study generalized Hankel operators ofthe form : ℱ 2 (| z | 2 ) → L 2 (| z | 2 ). Here, ( f ):= (Id–P l )( $ \bar z $ k f ) and P l is the projection onto A l 2 (ℂ, | z | 2 ):= cl(span{ $ \bar z $ m z n | m , n ∈ N , m ≤ l }). The investigations in this article extend the ones in [11] and [6], where the special cases l = 0 and l = 1 are considered, respectively. The main result is that the operators are not bounded for l < k – 1. The proof relies on a combinatoric argument and a generalization to general conjugate holomorphic L 2 symbols, generalizing arguments from [6], seems possible and is planned for future work (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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