arXiv subjects

P Jitendra Kumar Senapati

Publications and source records attributed to P Jitendra Kumar Senapati.

4 recordsLinked to original sources

arXiv2022

Restriction theorem for Fourier-Dunkl transform II: Paraboloid, sphere, and hyperboloid surfaces

This is a continuation of the paper "Restriction theorem for Fourier-Dunkl transform I: Cone surface, J. Pseudo-Differ. Oper. Appl. 14(1), Paper No. 5 (2023)", where the authors introduced and studied the Fourier-Dunkl transform on $\mathbb{R}^{n}\times\mathbb{R}^{d}$. The main novelty of this paper is that we here prove Strichartz's restriction theorem for the Fourier-Dunkl transform for certain surfaces, namely, paraboloid, sphere, and hyperboloid and its generalisation to the family of orthonormal functions. Finally, as an application of these restriction theorems, we establish versions of Strichartz estimates for orthonormal families of initial data associated with Schrödinger's propagator in the case of the Dunkl Laplacian and Klein-Gordon operator.

math.CA↗

arXiv2022

Restriction theorem for the Fourier-Dunkl transform I: Cone surface

In this article, we define the Fourier-Dunkl transform, which generalizes the Fourier transform. We prove Strichartz's restriction theorem for the Fourier-Dunkl transform for a cone-hyper-surface and its generalisation to the family of orthonormal functions. As an application of this restriction theorem, we derive the Strichartz inequality associated with the square root of Dunkl Laplacian for the family of orthonormal functions.

math.CA↗

arXiv2022

Strichartz inequality for orthonormal functions associated with Dunkl Laplacian and Hermite-Schrödinger operators

Strichartz inequality for the solutions of free Schrödinger equation associated with Dunkl Hermite operator $H_κ$ is generalized to any system of orthonormal functions with initial data. A relation between the kernels of Schrödinger propagators ($e^{-it H_κ}$ and $e^{itΔ_κ}$) associated with the Dunkl Hermite and Dunkl Laplacian operators is established using which corresponding Schtrichartz inequality for orthonormal functions associated with Dunkl Laplacian is obtained.

math.CA↗

arXiv2022

Sharp Strichartz type estimates for the Schrödinger equation associated with harmonic oscillator

In this article we study the Schrödinger equation associated with Harmonic oscillator in the form of Strichartz type inequality. We give simple proofs for Strichartz type inequalities using purely the $L^2 \to L^p$ operator norm estimates of the spectral projections associated harmonic oscillator proved in \cite{KT}. Our Strichartz type estimates are sharp in sense of regularity of initial data.

math.AP↗