Restriction Theorems and Strichartz Inequalities for the Laguerre Operator Involving Orthonormal Functions

In this paper, we prove restriction theorems for the Fourier–Laguerre transform and establish Strichartz estimates for the Schrödinger propagator e - i t L α for the Laguerre operator L α = - Δ - ∑ j = 1 n ( 2 α j + 1 x j ∂ ∂ x j ) + | x | 2 4 , α = ( α 1 , α 2 , … , α n ) ∈ ( - 1 2 , ∞ ) n on R + n...

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Bibliographic Details
Published in:The Journal of geometric analysis 2024-09, Vol.34 (9), Article 287
Main Authors: Feng, Guoxia, Song, Manli
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Global Analysis and Analysis on Manifolds
Mathematics
Mathematics and Statistics
Orthonormal functions
Theorems
Toruses
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Summary:In this paper, we prove restriction theorems for the Fourier–Laguerre transform and establish Strichartz estimates for the Schrödinger propagator e - i t L α for the Laguerre operator L α = - Δ - ∑ j = 1 n ( 2 α j + 1 x j ∂ ∂ x j ) + | x | 2 4 , α = ( α 1 , α 2 , … , α n ) ∈ ( - 1 2 , ∞ ) n on R + n involving systems of orthonormal functions. The proof is based on a combination of some known dispersive estimate and the argument in Nakamura [Trans Am Math Soc 373(2), 1455–1476 (2020)] on torus. As an application, we obtain the global well-posedness for the nonlinear Laguerre–Hartree equation in Schatten space.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-024-01740-4