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Perumal Muthukumar

Publications and source records attributed to Perumal Muthukumar.

5 recordsLinked to original sources
arXiv2020

Composition operators on Hardy spaces of the homogenous rooted trees

In \cite{CO-Tp-spaces}, the present authors initiated the study of composition operators on discrete analogue of generalized Hardy space $\mathbb{T}_{p}$ defined on a homogeneous rooted tree. In this article, we give equivalent conditions for the composition operator $C_ϕ$ to be bounded on $\mathbb{T}_{p}$ and on $\mathbb{T}_{p,0}$ spaces and compute their operator norm. We also characterize invertible composition operators as well as isometric composition operators on $\mathbb{T}_{p}$ and on $\mathbb{T}_{p,0}$ spaces. Also, we discuss the compactness of $C_ϕ$ on $\mathbb{T}_{p}$ and finally prove there are no compact composition operators on $\mathbb{T}_{p,0}$ spaces.

math.CV↗
arXiv2018

Weighted composition operators on the class of subordinate functions

In this article, we study the weighted composition operators preserving the class $\mathcal{P}_α$ of analytic functions subordinate to $\frac{1+αz}{1-z}$ for $|α|\leq 1, α\neq -1$. Some of its consequences and examples for some special cases are presented. Furthermore, we discuss about the fixed points of weighted composition operators.

math.FA↗
arXiv2018

Estimate for norm of a composition operator on the Hardy-Dirichlet space

By using the Schur test, we give some upper and lower estimates on the norm of a composition operator on $\mathcal{H}^2$, the space of Dirichlet series with square summable coefficients, for the inducing symbol $φ(s)=c_1+c_{q}q^{-s}$ where $q\geq 2$ is a fixed integer. We also give an estimate on the approximation numbers of such an operator.

math.FA↗
arXiv2016

Discrete Analogue of Generalized Hardy Spaces and Multiplication Operators on Homogenous Trees

In this article, we define discrete analogue of generalized Hardy spaces and its separable subspace on a homogenous rooted tree and study some of its properties such as completeness, inclusion relations with other spaces, separability, growth estimate for functions in these spaces and their consequences. Equivalent conditions for multiplication operators to be bounded and compact are also obtained. Furthermore, we discuss about point spectrum, approximate point spectrum and spectrum of multiplication operators and discuss when a multiplication operator is an isometry.

math.FA↗