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Fredholm composition operators and proper holomorphic mappings
Author(s) -
Cao Guangfu,
He Li,
Zhu Kehe
Publication year - 2019
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12300
Subject(s) - holomorphic function , mathematics , bounded function , composition (language) , holomorphic functional calculus , pure mathematics , hilbert space , fredholm theory , characterization (materials science) , domain (mathematical analysis) , composition operator , bounded operator , fredholm operator , operator (biology) , fredholm integral equation , mathematical analysis , discrete mathematics , compact operator , banach space , finite rank operator , multiplication operator , computer science , integral equation , physics , philosophy , repressor , linguistics , chemistry , biochemistry , transcription factor , programming language , extension (predicate logic) , gene , optics
Let H be a Hilbert space of holomorphic functions on a bounded domain Ω in C n . Under very mild conditions on Ω and H and using the theory of proper holomorphic maps, we present a characterization of holomorphic self‐maps φ : Ω → Ω such that the composition operator C φ is Fredholm on H .
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