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PreprintCC BY 4.0arXiv

Bohr-type inequalities for certain integral transforms of operator-valued analytic functions on shifted disc

  • Goutam Haldar
  • Kawsar Ali
  • Sujoy Majumder
  • Dilip Chandra Pramanik
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Abstract

In this paper, we investigate Bohr-type inequalities for certain integral transforms of some bounded holomorphic operator-valued functions defined on a shifted disc. More precisely, we consider functions f∈ H∞(Ωγ,ℬ(ℋ)), where ℬ(ℋ) denotes the space of bounded linear operators on a complex Hilbert space ℋ, and study the Bohr phenomena associated with the series representations in \eqref{e1.2a} and \eqref{e2.1}. Moreover, we determine the sharp radii Rγ>0 for which the corresponding majorant series satisfy the required inequalities for all |z|≤ Rγ. One of our main results extends some recent result due to Kumar and Sahoo \cite{Kumar-Sahoo-Meditarr-2023} to a large extent, and the other one is new in the literature

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Cite

BibTeXRIS
BibTeX
@misc{haldar2026bohrtype,
  title = {{Bohr-type inequalities for certain integral transforms of operator-valued analytic functions on shifted disc}},
  author = {Goutam Haldar and Kawsar Ali and Sujoy Majumder and Dilip Chandra Pramanik},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05194},
  eprint = {2610.05194},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05194},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Bohr-type inequalities for certain integral transforms of operator-valued analytic functions on shifted disc
AU  - Goutam Haldar
AU  - Kawsar Ali
AU  - Sujoy Majumder
AU  - Dilip Chandra Pramanik
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2610.05194
UR  - https://arxiv.org/abs/2610.05194
AB  - In this paper, we investigate Bohr-type inequalities for certain integral transforms of some bounded holomorphic operator-valued functions defined on a shifted disc. More precisely, we consider functions f∈ H^∞(Ω_γ,ℬ(ℋ)), where ℬ(ℋ) denotes the space of bounded linear operators on a complex Hilbert space ℋ, and study the Bohr phenomena associated with the series representations in \eqref{e1.2a} and \eqref{e2.1}. Moreover, we determine the sharp radii R_γ>0 for which the corresponding majorant series satisfy the required inequalities for all |z|≤ R_γ. One of our main results extends some recent result due to Kumar and Sahoo \cite{Kumar-Sahoo-Meditarr-2023} to a large extent, and the other one is new in the literature
ER  -