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Universal Composition Operators on the Hardy Space with Linear Fractional Symbols

Hassan, Aiham A
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1687181576013619

Abstract Details

2023, Doctor of Philosophy (Ph.D.), Bowling Green State University, Mathematics.
In this dissertation, we study universality of linear fractional composition operators on the Fréchet spaces H(𝔻) of holomorphic functions on the open unit disk 𝔻 and on the Hardy space H2. By definition, a sequence of operators Tn is universal if there is a vector x such that the sequence {x, T1x, T2x, …} is dense in the space. Specifically, we obtain necessary conditions and sufficient conditions for a sequence of composition operators Cϕn : H2 → H2 to be universal on the Hardy space H2 with linear fractional symbols ϕn(z) = (anz+bn)/(cnz+dn) taking the open unit disk 𝔻 into itself, where andn-bncn = 1. We show that if Cϕn is universal and the sequence dn/cn is bounded, then there is a subsequence ϕnk for which the sequences of coefficients, |ank|, |bnk|, |cnk|, |dnk| go to ∞, as k → ∞. In addition, the sequence |ank| - |cnk| goes to 0. Furthermore, we also provide sufficient conditions for Cϕn to be universal, in terms of the coefficients of ϕn. Lastly, in the special case when ϕn are automorphisms of the disk 𝔻, we show that Cϕn : H2 → H2 is universal on the Hardy space H2 if and only if the corresponding sequence Cϕn : H(𝔻) → H(𝔻) is universal on the Fréchet spaces H(𝔻)
Kit Chan, PhD (Committee Chair)
Apollos Nwauwa, PhD (Other)
Juan Bes, PhD (Committee Member)
So-Hsiang Chou, PhD (Committee Member)
81 p.
Mathematics
Hypercyclicity; Universal; Composition Operators; Hardy Space;

Recommended Citations

Citations

  • Hassan, A. A. (2023). Universal Composition Operators on the Hardy Space with Linear Fractional Symbols [Doctoral dissertation, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1687181576013619

    APA Style (7th edition)

  • Hassan, Aiham. Universal Composition Operators on the Hardy Space with Linear Fractional Symbols. 2023. Bowling Green State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1687181576013619.

    MLA Style (8th edition)

  • Hassan, Aiham. "Universal Composition Operators on the Hardy Space with Linear Fractional Symbols." Doctoral dissertation, Bowling Green State University, 2023. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1687181576013619

    Chicago Manual of Style (17th edition)

bgsu1687181576013619
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© 2023, all rights reserved.
This open access ETD is published by Bowling Green State University and OhioLINK.