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Abstract We obtain the optimal boundary behavior of the log-frequently hypercyclic functions with respect to the Taylor shift acting on H ( D ) in terms of average L p… Click to show full abstract
Abstract We obtain the optimal boundary behavior of the log-frequently hypercyclic functions with respect to the Taylor shift acting on H ( D ) in terms of average L p -norms. In passing we establish some new results on the growth of frequently or log-frequently hypercyclic functions for the differentiation operator on H ( C ) . All these results highlight the similarities and the differences between the lower and upper bounds on the growth of frequently and log-frequently hypercyclic functions, on the one hand in the case of the Taylor shift operator on H ( D ) and on the other hand in the case of the differentiation operator on H ( C ) .
Journal Title: Journal of Functional Analysis
Year Published: 2021
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