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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Composition–differentiation operators on the Hardy space
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by Mahsa Fatehi and Christopher N. B. Hammond PDF
Proc. Amer. Math. Soc. 148 (2020), 2893-2900 Request permission

Abstract:

Let $\varphi$ be a nonconstant analytic self-map of the open unit disk in $\mathbb {C}$, with $\|\varphi \|_{\infty }<1$. Consider the operator $D_{\varphi }$, acting on the Hardy space $H^{2}$, given by differentiation followed by composition with $\varphi$. We obtain results relating to the adjoint, norm, and spectrum of such an operator.
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Additional Information
  • Mahsa Fatehi
  • Affiliation: Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran
  • MR Author ID: 892247
  • Email: fatehimahsa@yahoo.com
  • Christopher N. B. Hammond
  • Affiliation: Department of Mathematics and Statistics, Connecticut College, New London, Connecticut 06320
  • MR Author ID: 728945
  • Email: cnham@conncoll.edu
  • Received by editor(s): August 2, 2019
  • Published electronically: March 18, 2020
  • Communicated by: Stephan Ramon Garcia
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 2893-2900
  • MSC (2010): Primary 47B38; Secondary 30H10, 47A05, 47A30, 47B33
  • DOI: https://doi.org/10.1090/proc/14898
  • MathSciNet review: 4099777