P. Ratnakumar

activity

20092024

most citedBenedick's theorem for the Heisenberg group

8 citations · 10 across the 4 of their papers we have counts for

collaborators

4 papers

math.FA2024

Non-isometric translation and modulation invariant Hilbert spaces

P. K. Ratnakumar, Joachim Toft, Jasson Vindas

Let $H$ be a Hilbert space of distributions on $R^{d}$ which contains at least one non-zero element in $D^{'} (R^{d})$ . If there is a constant $C_{0} > 0$ su…

math.FA2020

Translation and modulation invariant Hilbert spaces

Joachim Toft, Anupam Gumber, Ramesh Manna +1

We show that for any Hilbert space of distributions on $R^{d}$ which is translation and modulation invariant, is equal to $L^{2} (R^{d})$ , with the same norm apart from…

math.AP2014★ 2 cited

Functions operating on modulation spaces and nonlinear dispersive equations

Divyang G. Bhimani, P. K. Ratnakumar

The aim of this paper is two fold. We show that if a complex function $F$ on $\C$ operates in the modulation spaces $M^{p, 1} (R^{n})$ by composition, then $F$ is real analytic on $\R…

math.FA2009★ 8 cited

Benedick's theorem for the Heisenberg group

E. K. Narayanan, P. K. Ratnakumar

If $f$ is a compactly supported function on the Heisenberg group and the group Fourier transform $f^(λ)$ is a finite rank operator for all $λ$ then $f$ is the zero function.