arXiv subjects

Sunit Ghosh

Publications and source records attributed to Sunit Ghosh.

5 recordsLinked to original sources

arXiv2025

Restriction Theorem and Strichartz estimate for orthonormal functions associated with the Special Hermite Operator

Let $\mathcal{L}$ be the special Hermite operator on $\mathbb{C}^n$. As a continuation of the recent results in \cite{SG}, we establish new Strichartz estimates for systems of orthonormal functions associated with general flows of the form $e^{-it\phi(\mathcal{L})}$, where $ \phi : \mathbb{R}^{+} \to \mathbb{R} $ is a smooth function. Our approach relies on restriction estimates for the Fourier-special Hermite transform on the class of surfaces $\{(\lambda, \mu, \nu)\in \mathbb{R}\times\mathbb{N}_0^n\times\mathbb{N}_0^n : \lambda=\phi(2|\nu|+n)\}$. We also discuss the endpoint case of the orthonormal Strichartz estimate for the Schr\"{o}dinger propagator $e^{-it\mathcal{L}}$. Furthermore, we generalize restriction estimates for the special Hermite spectral projections in the context of trace ideals (Schatten spaces).

math.FA↗

arXiv2025

Heisenberg-Pauli-Weyl uncertainty principles for the fractional Dunkl transform on the real line

The aim of the paper is two-fold. First, we provide an explicit form of the functions for which equality holds for the uncertainty inequalities studied in \cite{Fei}. Second, we establish an $L^p$-type Heisenberg-Pauli-Weyl uncertainty principle for the fractional Dunkl transform, with $1 \leq p \leq 2$. For the case $p = 2$, we further derive a sharper uncertainty principle for the fractional Dunkl transform. Furthermore, we derive conditions leading to equality in both the uncertainty principles obtained.

math.FA↗

arXiv2024

On the Schatten exponent in orthonormal Strichartz estimate for the Dunkl operators

In \cite{PRA} and \cite{SSM} the orthonormal Strichartz estimates for the Schr\"odinger equation associated with the Dunkl Laplacian and the Dunkl-Hermite operator are obtained. In this article, we prove a necessary condition on the Schatten exponent for the above orthonormal Strichartz estimates, which turns out to be optimal for the Schr\"odinger equations associated with Laplacian and Hermite operator as a special case.

math.AP↗

arXiv2023

On local dispersive and Strichartz estimates for the Grushin operator

Let $G=-\Delta-|x|^2\partial_{t}^2$ denote the Grushin operator on $\mathbb{R}^{n+1}$. The aim of this paper is two fold. In the first part, due to the non-dispersive phenomena of the Grushin-Schr\"odinger equation on $\mathbb{R}^{n+1}$, we establish a local dispersive estimate by defining the Grushin-Schr\"odinger kernel on a suitable domain. As a corollary we obtain a local Strichartz estimate for the Grushin-Schr\"odinger equation. In the next part, we prove a restriction theorem with respect to the scaled Hermite-Fourier transform on $\mathbb{R}^{n+2}$ for certain surfaces in $\mathbb{N}_0^n\times\mathbb{R^*}\times \mathbb{R}$ and derive anisotropic Strichartz estimates for the Grushin-Schr\"{o}dinger equation and for the Grushin wave equation as well.

math.AP↗

arXiv2022

Restriction theorem for the Fourier-Hermite transform associated with the normalized Hermite polynomials and the Ornstein-Uhlenbeck-Schr\"odinger equation

In this article, we prove the analogue theorems of Stein-Tomas and Srtichartz on the discrete surface restrictions of Fourier-Hermite transforms associated with the normalized Hermite polynomials and obtain the Strichartz estimate for the system of orthonormal functions for the Ornstein-Uhlenbeck operator $L=-\frac{1}{2}\Delta+\langle x, \nabla\rangle$ on $\mathbb{R}^n$. Further, we show an optimal behavior of the constant in the Strichartz estimate as limit of a large number of functions.

math.CA↗