Pratyoosh Kumar

activity

20122020

most citedFourier restriction Theorem and characterization of weak

L^{2}

eigenfunctions of the Laplace--Beltrami operator

9 citations · 12 across the 5 of their papers we have counts for

collaborators

5 papers

math.FA2020

Dynamics of semigroups generated by analytic functions of the Laplacian on Homogeneous Trees

Pratyoosh Kumar, Sumit Kumar Rano

Let $f$ be a non-constant complex-valued analytic function defined on a connected, open set containing the $L^{p}$ -spectrum of the Laplacian $L$ on a homogeneous tree. In th…

math.FA2019

A Theorem of Roe and Strichartz on homogeneous trees

Pratyoosh Kumar, Sumit Kumar Rano

In 1980, J. Roe proved that if ${f_{k}}_{k \in Z}$ is doubly infinite sequence of functions in $R$ which is uniformly bounded and satisfies $(d f_{k} / d x) = f_{k + 1}$ …

math.FA2018★ 1 cited

Analysis of $L^{p}$ -type estimates of Poisson transform on Homogeneous Trees

Pratyoosh Kumar, Sumit Kumar Rano

In this article we prove the restriction theorem for Helgason-Fourier transform on homogeneous tree. Our proof is based on the duality argument and the norm estimates of Poisson tr…

math.FA2012★ 9 cited

Fourier restriction Theorem and characterization of weak $L^{2}$ eigenfunctions of the Laplace--Beltrami operator

Pratyoosh Kumar

In this paper we prove the Fourier restriction theorem for $p = 2$ on Riemannian symmetric spaces of noncompact type with real rank one which extends the earlier result proved in \ci…

math.FA2012★ 2 cited

Characterization of almost $L^{p}$ -eigenfunctions of the Laplace-Beltrami operator

Pratyoosh Kumar, Swagato K. Ray, Rudra P. Sarkar

In \cite{Roe} Roe proved that if a doubly-infinite sequence ${f_{k}}$ of functions on $R$ satisfies $f_{k + 1} = (d f_{k} / d x)$ and $∣ f_{k} (x) ∣ \leq M$ for all $k = 0, \pm 1, \pm 2, ...$ and…

Dynamics of semigroups generated by analytic functions of the Laplacian on Homogeneous Trees

A Theorem of Roe and Strichartz on homogeneous trees

Analysis of Lp-type estimates of Poisson transform on Homogeneous Trees

Fourier restriction Theorem and characterization of weak L2 eigenfunctions of the Laplace--Beltrami operator

Characterization of almost Lp-eigenfunctions of the Laplace-Beltrami operator

Analysis of $L^{p}$ -type estimates of Poisson transform on Homogeneous Trees

Fourier restriction Theorem and characterization of weak $L^{2}$ eigenfunctions of the Laplace--Beltrami operator

Characterization of almost $L^{p}$ -eigenfunctions of the Laplace-Beltrami operator