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 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 Cn. 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 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 Cn. 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