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Abstract
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We study the differentiation operator acting on discrete function spaces,
that is, spaces of functions defined on an infinite rooted tree. We discuss,
through its connection with composition operators, the boundedness and
compactness of this operator. In addition, we discuss the operator norm and
spectrum and consider when such an operator can be an isometry. We then
apply these results to the operator acting on the discrete Lipschitz space and
weighted Banach spaces, as well as the Hardy spaces defined on homogeneous
trees.
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Keywords
differentiation, discrete function spaces, infinite trees
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Mathematical Subject Classification
Primary: 47B38
Secondary: 05C05
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Milestones
Received: 19 June 2021
Revised: 4 August 2021
Accepted: 5 August 2021
Published: 14 March 2022
Communicated by Stephan Garcia
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