Strichartz estimates and Fourier restriction theorems on the Heisenberg group

DOI10.1007/s00041-021-09822-5zbMath1460.35365arXiv1911.03729OpenAlexW3131033510MaRDI QIDQ2658737

Davide Barilari, Isabelle Gallagher, Hajer Bahouri

Publication date: 24 March 2021

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.03729

zbMATH Keywords

non-commutative Fourier transformanisotropic Strichartz estimatetotally non-dispersive evolution equation

Mathematics Subject Classification ID

Wave equation (35L05) PDEs in connection with quantum mechanics (35Q40) Initial value problems for second-order hyperbolic equations (35L15) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Related Items (3)

Probabilistic local well-posedness for the Schrödinger equation posed for the Grushin Laplacian ⋮ Decay estimates for a class of wave equations on the Heisenberg group ⋮ Restriction theorem fails for the Fourier-Hermite transform associated with the normalized Hermite polynomials with respect to a discrete surface

Cites Work

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• A restriction theorem for Grushin operators
• Dispersive estimates for the Schrödinger operator on step-2 stratified Lie groups
• Nonlinear Schrödinger equation on real hyperbolic spaces
• A restriction theorem for the Heisenberg group
• The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups
• Deux cours d'analyse harmonique. École d'Été d'Analyse Harmonique de Tunis, 1984
• Quantum mechanics and partial differential equations
• Hypoelliptic differential operators and nilpotent groups
• Least action principle, heat propagation and subelliptic estimates on certain nilpotent groups
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I: Schrödinger equations
• A remark on Schrödinger operators
• Generalized Strichartz inequalities for the wave equation
• Dispersion for the wave equation inside strictly convex domains. I: The Friedlander model case
• Tempered distributions and Fourier transform on the Heisenberg group
• \(L^p\) joint eigenfunction bounds on quaternionic spheres
• A frequency space for the Heisenberg group
• A restriction theorem for Métivier groups
• Restriction estimates via the derivatives of the heat semigroup and connection with dispersive estimates
• Inequalities for strongly singular convolution operators
• Phase-space analysis and pseudodifferential calculus on the Heisenberg group
• A restriction theorem for the H-type groups
• The wave equation on the heisenberg group
• Fourier Analysis and Nonlinear Partial Differential Equations
• A functional calculus for Rockland operators on nilpotent Lie groups
• Equations de Schrödinger non linéaires en dimension deux
• Endpoint Strichartz estimates
• Dispersive estimates with loss of derivatives via the heat semigroup and the wave operator
• Dispersive and Strichartz estimates on H-type groups
• Strichartz inequalities and the nonlinear Schrodinger equation on compact manifolds
• Equations d'ondes quasilineaires et estimations de Strichartz
• Newton polygons as lattice points
• Mean Convergence of Expansions in Laguerre and Hermite Series
• Besov spaces and Strichartz estimates on the Heisenberg group
• Maximal functions associated to filtrations
• Paraproduct on the Heisenberg group and applications
• A restriction theorem for the Fourier transform

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