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Covering Results and Perturbed Roper–Suffridge Operators

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Abstract

This work is devoted to the advanced study of Roper–Suffridge type extension operators. For a given non-normalized spirallike function (with respect to an interior or boundary point) on the open unit disk of the complex plane, we construct perturbed extension operators in a certain class of Banach spaces and prove that these operators preserve the spirallikeness property. In addition, we present an extension operator for semigroup generators. We use a new geometric approach based on the connection between spirallike mappings and one-parameter continuous semigroups. It turns out that the new one-dimensional covering results established below are crucial for our investigation.

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Authors and Affiliations

  1. Department of Mathematics, Ort Braude College, Karmiel, 21982, Israel

    Mark Elin & Marina Levenshtein

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  1. Mark Elin
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  2. Marina Levenshtein
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Correspondence to Mark Elin.

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Communicated by David Shoikhet.

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Elin, M., Levenshtein, M. Covering Results and Perturbed Roper–Suffridge Operators. Complex Anal. Oper. Theory 8, 25–36 (2014). https://doi.org/10.1007/s11785-012-0259-1

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  • DOI: https://doi.org/10.1007/s11785-012-0259-1

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