Ramlal Debnath

activity

20192026

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6 papers · 1 filter

math.FA2025

Inner and characteristic functions in polydiscs

Ramlal Debnath, Deepak K. Pradhan, Jaydeb Sarkar

Characteristic functions of linear operators are analytic functions that serve as complete unitary invariants. Such functions, as long as they are built in a natural and canonical…

math.FA2024

Two problems on submodules of $H^{2} (D^{n})$

Ramlal Debnath, Srijan Sarkar

Given any shift-invariant closed subspace $S$ (aka submodule) of the Hardy space over the unit polydisc $H^{2} (D^{n})$ (where $n \geq 2$ ), let $R_{z_j}:=M_{z_j}|_{\m…

math.FA2023

Pairs of inner projections and two applications

Ramlal Debnath, Deepak K. Pradhan, Jaydeb Sarkar

Orthogonal projections onto closed subspaces of $H^{2} (D^{n})$ of the form $φ H^{2} (D^{n})$ for inner functions $φ$ on $D^{n}$ are referred to as inner projections,…

math.FA2022

$\clw$-hypercontractions and their model

Monojit Bhattacharjee, B. Krishna Das, Ramlal Debnath +1

We revisit the study of $ω$ -hypercontractions corresponding to a single weight sequence $ω = {ω_{k}}_{k \geq 0}$ introduced by Olofsson in \cite{O} and find an analogue of Nagy-Foias c…

math.FA2021

Beurling quotient modules on the polydisc

Monojit Bhattacharjee, B. Krishna Das, Ramlal Debnath +1

Let $H^{2} (D^{n})$ denote the Hardy space over the polydisc $D^{n}$ , $n \geq 2$ . A closed subspace $Q \subseteq H^{2} (D^{n})$ is called Beurling quotient…

math.FA2019

Factorizations of Schur functions

Ramlal Debnath, Jaydeb Sarkar

The Schur class, denoted by $S (D)$ , is the set of all functions analytic and bounded by one in modulus in the open unit disc $D$ in the complex plane $\…