P. Muthukumar

@iitk.ac.in

Assistant Professor, Department of Mathematics and Statistics
Indian Institute of Technology Kanpur

P. Muthukumar


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https://researchid.co/pmuthukumar

RESEARCH INTERESTS

Analytic Function Theory, (Discrete) Operator Theory.
11

Scopus Publications

87

Scholar Citations

6

Scholar h-index

5

Scholar i10-index

Scopus Publications

  • Composition operators between Beurling subspaces of Hardy space
    V.A. Anjali, P. Muthukumar, P. Shankar
    Journal of Mathematical Analysis and Applications, 2026
  • Automorphisms of subalgebras of bounded analytic functions
    Kanha Behera, Rahul Maurya, P. Muthukumar
    Journal of Mathematical Analysis and Applications, 2025
  • Weighted Composition Operators Between Weighted Hardy Spaces on Rooted Trees
    P. Muthukumar, Ajay K. Sharma, Vivek Kumar
    Mediterranean Journal of Mathematics, 2023
  • Model spaces invariant under composition operators
    P. Muthukumar, Jaydeb Sarkar
    Canadian Mathematical Bulletin, 2023
    Given a holomorphic self-map $\\varphi $ of $\\mathbb {D}$ (the open unit disc in $\\mathbb {C}$ ), the composition operator $C_{\\varphi } f = f \\circ \\varphi $ , $f \\in H^2(\\mathbb {\\mathbb {D}})$ , defines a bounded linear operator on the Hardy space $H^2(\\mathbb {\\mathbb {D}})$ . The model spaces are the backward shift-invariant closed subspaces of $H^2(\\mathbb {\\mathbb {D}})$ , which are canonically associated with inner functions. In this paper, we study model spaces that are invariant under composition operators. Emphasis is put on finite-dimensional model spaces, affine transformations, and linear fractional transformations.
  • Multiplication Operators Between Discrete Hardy Spaces on Rooted Trees
    P. Muthukumar, P. Shankar
    Lobachevskii Journal of Mathematics, 2022
    Muthukumar and Ponnusamy [9] studied the multiplication operators on $$\mathbb{T}_{p}$$ spaces. In this article, we mainly consider multiplication operators between $$\mathbb{T}_{p}$$ and $$\mathbb{T}_{q}$$ ( $$p\neq q$$ ). In particular, we characterize bounded and compact multiplication operators from $$\mathbb{T}_{p}$$ to $$\mathbb{T}_{q}$$ . For $$p\neq q$$ , we prove that there are no invertible multiplication operators from $$\mathbb{T}_{p}$$ to $$\mathbb{T}_{q}$$ and also there are no isometric multiplication operators from $$\mathbb{T}_{p}$$ to $$\mathbb{T}_{q}$$ . Finally, we discuss about fixed points of a multiplication operator on $$\mathbb{T}_{p}$$ .
  • BEURLING TYPE INVARIANT SUBSPACES OF COMPOSITION OPERATORS
    Snehasish Bose, , P. Muthukumar, Jaydeb Sarkar, , and
    Journal of Operator Theory, 2021
    The aim of this paper is to answer the following question concerning invariant subspaces of composition operators: characterize φ, holomorphic self maps of D, and inner functions θ∈H∞(D) such that the Beurling type invariant subspace θH2 is an invariant subspace for Cφ. We prove the following result: Cφ(θH2)⊆θH2 if and only if θ∘φθ∈S(D). This classification also allows us to recover or improve some known results on Beurling type invariant subspaces of composition operators.
  • Composition operators on Hardy spaces of the homogenous rooted trees
    Perumal Muthukumar, Saminathan Ponnusamy
    Monatshefte Fur Mathematik, 2020
  • Estimate for Norm of a Composition Operator on the Hardy–Dirichlet Space
    Perumal Muthukumar, Saminathan Ponnusamy, Hervé Queffélec
    Integral Equations and Operator Theory, 2018
  • Weighted composition operators on the class of subordinate functions
    Perumal Muthukumar, Saminathan Ponnusamy
    Rocky Mountain Journal of Mathematics, 2018
    In this article, we study the weighted composition operators preserving the class $\\mathcal{P}_{\\alpha}$ of analytic functions subordinate to $\\frac{1+\\alpha z}{1-z}$ for $|\\alpha|\\leq 1, \\alpha \\neq -1$. Some of its consequences and examples for some special cases are presented. Furthermore, we discuss about the fixed points of weighted composition operators.
  • Composition Operators on the Discrete Analogue of Generalized Hardy Space on Homogenous Trees
    Perumal Muthukumar, Saminathan Ponnusamy
    Bulletin of the Malaysian Mathematical Sciences Society, 2017
  • Discrete analogue of generalized Hardy spaces and multiplication operators on homogenous trees
    Perumal Muthukumar, Saminathan Ponnusamy
    Analysis and Mathematical Physics, 2017

RECENT SCHOLAR PUBLICATIONS

  • Applications of Reproducing Kernels in composition operators
    P Kumari, P Muthukumar, A Rasila
    arXiv preprint arXiv:2601.19596 , 2026
    2026
  • Automorphisms of subalgebras of bounded analytic functions
    K Behera, R Maurya, P Muthukumar
    Journal of Mathematical Analysis and Applications 552 (2), 129804 , 2025
    2025
  • Multiplicative operators on analytic function spaces
    K Behera, J Liu, P Muthukumar
    arXiv preprint arXiv:2512.05798 , 2025
    2025
  • Composition operators between Beurling subspaces of Hardy space
    VA Anjali, P Muthukumar, P Shankar
    Journal of Mathematical Analysis and Applications, 129929 , 2025
    2025
  • Finite-dimensional model spaces invariant under composition operators
    P Muthukumar, J Sarkar, B Undrakh
    arXiv preprint arXiv:2507.09666 , 2025
    2025
    Citations: 1
  • New norm estimate for composition operators
    P Kumari, P Muthukumar, J Sarkar
    https://arxiv.org/abs/2509.14655 , 2025
    2025
  • Weighted composition operators between weighted Hardy spaces on rooted trees
    P Muthukumar, AK Sharma, V Kumar
    Mediterranean Journal of Mathematics 20 (61), 21pp , 2023
    2023
    Citations: 1
  • Multiplication operators between discrete Hardy spaces on rooted trees
    P Muthukumar, P Shankar
    Lobachevskii Journal of Mathematics 43 (11), 3252–3263 , 2022
    2022
    Citations: 2
  • Model spaces invariant under composition operators
    P Muthukumar, J Sarkar
    Canadian Mathematical Bulletin 66 (1), 204--217 , 2021
    2021
    Citations: 7
  • Beurling type invariant subspaces of composition operators
    S Bose, P Muthukumar, J Sarkar
    Journal of Operator Theory 86 (2), 425-438 , 2021
    2021
    Citations: 12
  • Composition operators on Hardy spaces of the homogenous rooted trees
    P Muthukumar, S Ponnusamy
    Monatshefte für Mathematik 192 (3), 721–743 , 2020
    2020
    Citations: 13
  • A study of operators on the discrete analogue of Hardy spaces on homogeneous trees and on other structures.
    P Muthukumar
    Indian statistical Institute, Bangalore , 2019
    2019
  • Estimate for Norm of a Composition Operator on the Hardy–Dirichlet Space
    P Muthukumar, S Ponnusamy, H Queffélec
    Integral Equations and Operator Theory 90 (1), 12pp , 2018
    2018
    Citations: 10
  • Weighted composition operators on the class of subordinate functions
    P Muthukumar, S Ponnusamy
    Rocky Mountain Journal of Mathematics 48 (6), 2055-2068 , 2018
    2018
    Citations: 2
  • Composition operators on the discrete analogue of generalized Hardy space on homogenous trees
    P Muthukumar, S Ponnusamy
    Bulletin of the Malaysian Mathematical Sciences Society 40 (4), 1801-1815 , 2017
    2017
    Citations: 20
  • Discrete analogue of generalized Hardy spaces and multiplication operators on homogenous trees
    P Muthukumar, S Ponnusamy
    Analysis and Mathematical Physics 7 (3), 267-283 , 2017
    2017
    Citations: 19

MOST CITED SCHOLAR PUBLICATIONS

  • Composition operators on the discrete analogue of generalized Hardy space on homogenous trees
    P Muthukumar, S Ponnusamy
    Bulletin of the Malaysian Mathematical Sciences Society 40 (4), 1801-1815 , 2017
    2017
    Citations: 20
  • Discrete analogue of generalized Hardy spaces and multiplication operators on homogenous trees
    P Muthukumar, S Ponnusamy
    Analysis and Mathematical Physics 7 (3), 267-283 , 2017
    2017
    Citations: 19
  • Composition operators on Hardy spaces of the homogenous rooted trees
    P Muthukumar, S Ponnusamy
    Monatshefte für Mathematik 192 (3), 721–743 , 2020
    2020
    Citations: 13
  • Beurling type invariant subspaces of composition operators
    S Bose, P Muthukumar, J Sarkar
    Journal of Operator Theory 86 (2), 425-438 , 2021
    2021
    Citations: 12
  • Estimate for Norm of a Composition Operator on the Hardy–Dirichlet Space
    P Muthukumar, S Ponnusamy, H Queffélec
    Integral Equations and Operator Theory 90 (1), 12pp , 2018
    2018
    Citations: 10
  • Model spaces invariant under composition operators
    P Muthukumar, J Sarkar
    Canadian Mathematical Bulletin 66 (1), 204--217 , 2021
    2021
    Citations: 7
  • Multiplication operators between discrete Hardy spaces on rooted trees
    P Muthukumar, P Shankar
    Lobachevskii Journal of Mathematics 43 (11), 3252–3263 , 2022
    2022
    Citations: 2
  • Weighted composition operators on the class of subordinate functions
    P Muthukumar, S Ponnusamy
    Rocky Mountain Journal of Mathematics 48 (6), 2055-2068 , 2018
    2018
    Citations: 2
  • Finite-dimensional model spaces invariant under composition operators
    P Muthukumar, J Sarkar, B Undrakh
    arXiv preprint arXiv:2507.09666 , 2025
    2025
    Citations: 1
  • Weighted composition operators between weighted Hardy spaces on rooted trees
    P Muthukumar, AK Sharma, V Kumar
    Mediterranean Journal of Mathematics 20 (61), 21pp , 2023
    2023
    Citations: 1
  • Applications of Reproducing Kernels in composition operators
    P Kumari, P Muthukumar, A Rasila
    arXiv preprint arXiv:2601.19596 , 2026
    2026
  • Automorphisms of subalgebras of bounded analytic functions
    K Behera, R Maurya, P Muthukumar
    Journal of Mathematical Analysis and Applications 552 (2), 129804 , 2025
    2025
  • Multiplicative operators on analytic function spaces
    K Behera, J Liu, P Muthukumar
    arXiv preprint arXiv:2512.05798 , 2025
    2025
  • Composition operators between Beurling subspaces of Hardy space
    VA Anjali, P Muthukumar, P Shankar
    Journal of Mathematical Analysis and Applications, 129929 , 2025
    2025
  • New norm estimate for composition operators
    P Kumari, P Muthukumar, J Sarkar
    https://arxiv.org/abs/2509.14655 , 2025
    2025
  • A study of operators on the discrete analogue of Hardy spaces on homogeneous trees and on other structures.
    P Muthukumar
    Indian statistical Institute, Bangalore , 2019
    2019