数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (5): 1931-1944.doi: 10.1007/s10473-024-0517-0

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TOEPLITZ DETERMINANTS IN ONE AND HIGHER DIMENSIONS*

Surya Giri, S. Sivaprasad Kumar   

  1. Department of Applied Mathematics, Delhi Technological University, New Delhi 110042, India
  • 收稿日期:2022-11-11 修回日期:2024-02-02 出版日期:2024-10-25 发布日期:2024-10-22
  • 通讯作者: †S. Sivaprasad Kumar, E-mail,: spkumar@dce.ac.in
  • 作者简介:Surya Giri, E-mail,: suryagiri456@gmail.com
  • 基金资助:
    Univer-sity Grant Commission, New Delhi, India under UGC-Ref. No. 1112/(CSIR-UGC NET JUNE 2019).

TOEPLITZ DETERMINANTS IN ONE AND HIGHER DIMENSIONS*

Surya Giri, S. Sivaprasad Kumar   

  1. Department of Applied Mathematics, Delhi Technological University, New Delhi 110042, India
  • Received:2022-11-11 Revised:2024-02-02 Online:2024-10-25 Published:2024-10-22
  • Contact: †S. Sivaprasad Kumar, E-mail,: spkumar@dce.ac.in
  • About author:Surya Giri, E-mail,: suryagiri456@gmail.com
  • Supported by:
    Univer-sity Grant Commission, New Delhi, India under UGC-Ref. No. 1112/(CSIR-UGC NET JUNE 2019).

摘要: In this study, we derive the sharp bounds of certain Toeplitz determinants whose entries are the coefficients of holomorphic functions belonging to a class defined on the unit disk $\mathbb{U}$. Furthermore, these results are extended to a class of holomorphic functions on the unit ball in a complex Banach space and on the unit polydisc in $\mathbb{C}^n$. The obtained results provide the bounds of Toeplitz determinants in higher dimensions for various subclasses of normalized univalent functions.

关键词: holomorphic mappings, starlike mappings, Toeplitz determinants, coefficient inequalities

Abstract: In this study, we derive the sharp bounds of certain Toeplitz determinants whose entries are the coefficients of holomorphic functions belonging to a class defined on the unit disk $\mathbb{U}$. Furthermore, these results are extended to a class of holomorphic functions on the unit ball in a complex Banach space and on the unit polydisc in $\mathbb{C}^n$. The obtained results provide the bounds of Toeplitz determinants in higher dimensions for various subclasses of normalized univalent functions.

Key words: holomorphic mappings, starlike mappings, Toeplitz determinants, coefficient inequalities

中图分类号: 

  • 32H02