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The
differentiation operator on discrete function spaces of a
tree
Robert F. Allen and Colin M. Jackson
Vol. 15 (2022), No. 1, 163–184
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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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Authors |
| Robert F. Allen | |
| Department of Mathematics and
Statistics University of Wisconsin La Crosse, WI United States |
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| Colin M. Jackson | |
| Department of Mathematics University of Colorado Boulder, CO United States |
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