Remarks on Composition Operators on the Newton Space

Eungil Ko; Ji Eun Lee; Jongrak Lee

doi:10.1007/s00009-022-02130-2

Remarks on Composition Operators on the Newton Space

Eungil Ko, Ji Eun Lee, Jongrak Lee

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper, we study properties of composition operators on the Newton space, i.e., the Hilbert space of analytic functions which have the Newton polynomials as an orthonormal basis. In particular, we focus on various properties of the composition operator C_T induced by T on the Newton space where T(z) = z+ 1. Moreover, we examine conditions on the symbol φ for the induced composition operator C_φ which belongs to Newton space N²(P) where φ is a linear fraction transformation or an analytic function of P. Finally, we concern complex symmetric composition operators on the Newton space N²(P).

Original language	English
Article number	205
Journal	Mediterranean Journal of Mathematics
Volume	19
Issue number	5
DOIs	https://doi.org/10.1007/s00009-022-02130-2
State	Published - Oct 2022

Keywords

Newton space
complex symmetric operator
composition operator

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10.1007/s00009-022-02130-2

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title = "Remarks on Composition Operators on the Newton Space",

abstract = "In this paper, we study properties of composition operators on the Newton space, i.e., the Hilbert space of analytic functions which have the Newton polynomials as an orthonormal basis. In particular, we focus on various properties of the composition operator CT induced by T on the Newton space where T(z) = z+ 1. Moreover, we examine conditions on the symbol φ for the induced composition operator Cφ which belongs to Newton space N2(P) where φ is a linear fraction transformation or an analytic function of P. Finally, we concern complex symmetric composition operators on the Newton space N2(P).",

keywords = "Newton space, complex symmetric operator, composition operator",

author = "Eungil Ko and Lee, {Ji Eun} and Jongrak Lee",

note = "Funding Information: The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (no. 2019R1F1A1058633) the Ministry of Education (no. 2019R1A6A1A11051177). The second author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (no. 2019R1A2C1002653). The third author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (no. 2021R1C1C1008713). Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2022",

month = oct,

doi = "10.1007/s00009-022-02130-2",

language = "English",

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journal = "Mediterranean Journal of Mathematics",

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AU - Lee, Jongrak

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N2 - In this paper, we study properties of composition operators on the Newton space, i.e., the Hilbert space of analytic functions which have the Newton polynomials as an orthonormal basis. In particular, we focus on various properties of the composition operator CT induced by T on the Newton space where T(z) = z+ 1. Moreover, we examine conditions on the symbol φ for the induced composition operator Cφ which belongs to Newton space N2(P) where φ is a linear fraction transformation or an analytic function of P. Finally, we concern complex symmetric composition operators on the Newton space N2(P).

AB - In this paper, we study properties of composition operators on the Newton space, i.e., the Hilbert space of analytic functions which have the Newton polynomials as an orthonormal basis. In particular, we focus on various properties of the composition operator CT induced by T on the Newton space where T(z) = z+ 1. Moreover, we examine conditions on the symbol φ for the induced composition operator Cφ which belongs to Newton space N2(P) where φ is a linear fraction transformation or an analytic function of P. Finally, we concern complex symmetric composition operators on the Newton space N2(P).

KW - Newton space

KW - complex symmetric operator

KW - composition operator

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JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 5

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ER -

Remarks on Composition Operators on the Newton Space

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