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PreprintCC0arXiv

Interpolation by Rational ΓE(3; 3; 1, 1, 1)-Inner Function and Rational ΓE(3; 2; 1, 2)-Inner Function

  • Avijit Pal
  • Bhaskar Paul
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Abstract

We study several function-theoretic aspects of the domains GE(3;3;1,1,1) and GE(3;2;1,2). We introduce and investigate the notions of ΓE(3;3;1,1,1)-inner functions and ΓE(3;2;1,2)-inner functions, and establish their relationships with ΓE(2;2;1,1)-inner functions and ΓE(2;1;2)-inner functions. We provide explicit constructions and representations of rational ΓE(3;3;1,1,1)-inner functions and rational ΓE(3;2;1,2)-inner functions. As an application of these results, we obtain partial solutions to the associated interpolation problems and construct explicit rational inner interpolants for interpolation data lying in suitable subsets of GE(3;3;1,1,1) and GE(3;2;1,2), respectively.

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Cite

BibTeXRIS
BibTeX
@misc{pal2026interpolation,
  title = {{Interpolation by Rational $Γ_E(3; 3; 1, 1, 1)$-Inner Function and Rational $Γ_E(3; 2; 1, 2)$-Inner Function}},
  author = {Avijit Pal and Bhaskar Paul},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16779},
  eprint = {2610.16779},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16779},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Interpolation by Rational Γ_E(3; 3; 1, 1, 1)-Inner Function and Rational Γ_E(3; 2; 1, 2)-Inner Function
AU  - Avijit Pal
AU  - Bhaskar Paul
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16779
UR  - https://arxiv.org/abs/2610.16779
AB  - We study several function-theoretic aspects of the domains G_E(3;3;1,1,1) and G_E(3;2;1,2). We introduce and investigate the notions of Γ_E(3;3;1,1,1)-inner functions and Γ_E(3;2;1,2)-inner functions, and establish their relationships with Γ_E(2;2;1,1)-inner functions and Γ_E(2;1;2)-inner functions. We provide explicit constructions and representations of rational Γ_E(3;3;1,1,1)-inner functions and rational Γ_E(3;2;1,2)-inner functions. As an application of these results, we obtain partial solutions to the associated interpolation problems and construct explicit rational inner interpolants for interpolation data lying in suitable subsets of G_E(3;3;1,1,1) and G_E(3;2;1,2), respectively.
ER  -