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

4 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

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Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Keywords

Newton space
complex symmetric operator
composition operator

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10.1007/s00009-022-02130-2

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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).

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ER -

Remarks on Composition Operators on the Newton Space

Abstract

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Keywords

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