P. Muthukumar
@iitk.ac.in
Assistant Professor, Department of Mathematics and Statistics
Indian Institute of Technology Kanpur
RESEARCH INTERESTS
Analytic Function Theory, (Discrete) Operator Theory.
Scopus Publications
Scholar Citations
Scholar h-index
Scholar i10-index
Scopus Publications
P. Muthukumar, Ajay K. Sharma, and Vivek Kumar
Springer Science and Business Media LLC
P. Muthukumar and P. Shankar
Pleiades Publishing Ltd
P. Muthukumar and Jaydeb Sarkar
Canadian Mathematical Society
Abstract 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.
Snehasish Bose, , P. Muthukumar, Jaydeb Sarkar, , and
Theta Foundation
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.
Perumal Muthukumar and Saminathan Ponnusamy
Springer Science and Business Media LLC
Perumal Muthukumar, Saminathan Ponnusamy, and Hervé Queffélec
Springer Science and Business Media LLC
Perumal Muthukumar and Saminathan Ponnusamy
Rocky Mountain Mathematics Consortium
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.
Perumal Muthukumar and Saminathan Ponnusamy
Springer Science and Business Media LLC
Perumal Muthukumar and Saminathan Ponnusamy
Springer Science and Business Media LLC