Orthonormal Strichartz estimate for dispersive equations with potentials
A Hoshiya - Journal of Functional Analysis, 2024 - Elsevier
In this paper we prove the orthonormal Strichartz estimates for the higher order and
fractional Schrödinger, wave, Klein-Gordon and Dirac equations with potentials. As in the …
fractional Schrödinger, wave, Klein-Gordon and Dirac equations with potentials. As in the …
Restriction Theorem for the Fourier–Dunkl Transform and Its Applications to Strichartz Inequalities
In this article, we address the following Strichartz's restriction problem: For a given surface S
embedded in R n× R d with n+ d≥ 2, for what values of 1≤ p< 2, do we have∫ S| f^(ξ, ζ)| 2 …
embedded in R n× R d with n+ d≥ 2, for what values of 1≤ p< 2, do we have∫ S| f^(ξ, ζ)| 2 …
Orthonormal Strichartz estimates for Schr\" odinger operator and their applications to infinitely many particle systems
A Hoshiya - arXiv preprint arXiv:2312.08314, 2023 - arxiv.org
We develop an abstract perturbation theory for the orthonormal Strichartz estimates, which
were first studied by Frank-Lewin-Lieb-Seiringer. The method used in the proof is based on …
were first studied by Frank-Lewin-Lieb-Seiringer. The method used in the proof is based on …
Strichartz estimates for the -generalized Laguerre operators
K Taira, H Tamori - arXiv preprint arXiv:2308.16815, 2023 - arxiv.org
In this paper, we prove Strichartz estimates for the $(k, a) $-generalized Laguerre operators
$ a^{-1}(-| x|^{2-a}\Delta_k+| x|^ a) $ which were introduced by Ben Sa\"{\i} d-Kobayashi-{\0} …
$ a^{-1}(-| x|^{2-a}\Delta_k+| x|^ a) $ which were introduced by Ben Sa\"{\i} d-Kobayashi-{\0} …
Uniform resolvent and orthonormal Strichartz estimates for repulsive Hamiltonian
A Hoshiya - arXiv preprint arXiv:2407.05707, 2024 - arxiv.org
We consider the uniform resolvent and orthonormal Strichartz estimates for the Schr\"
odinger operator. First we prove the Keel-Tao type theorem for the orthonormal Strichartz …
odinger operator. First we prove the Keel-Tao type theorem for the orthonormal Strichartz …
Decay estimates for a class of Dunkl wave equations
C Luo, SS Mondal, M Song - arXiv preprint arXiv:2407.06949, 2024 - arxiv.org
Let $\Delta_\kappa $ be the Dunkl Laplacian on $\mathbb {R}^ n $ and $\phi:\mathbb
{R}^+\to\mathbb {R} $ is a smooth function. The aim of this manuscript is twofold. First, we …
{R}^+\to\mathbb {R} $ is a smooth function. The aim of this manuscript is twofold. First, we …
Orthonormal Strichartz inequalities and their applications on abstract measure spaces
G Feng, SS Mondal, M Song, H Wu - arXiv preprint arXiv:2409.14044, 2024 - arxiv.org
The main objective of this paper is to extend certain fundamental inequalities from a single
function to a family of orthonormal systems. In the first part of the paper, we consider a non …
function to a family of orthonormal systems. In the first part of the paper, we consider a non …
Restriction theorems and Strichartz inequalities for the Laguerre operator involving orthonormal functions
G Feng, M Song - The Journal of Geometric Analysis, 2024 - Springer
In this paper, we prove restriction theorems for the Fourier–Laguerre transform and establish
Strichartz estimates for the Schrödinger propagator e-it L α for the Laguerre operator L α=-Δ …
Strichartz estimates for the Schrödinger propagator e-it L α for the Laguerre operator L α=-Δ …
Improved spectral cluster bounds for orthonormal systems
T Ren, A Zhang - Forum Mathematicum, 2024 - degruyter.com
We improve the work [RL Frank and J. Sabin, Spectral cluster bounds for orthonormal
systems and oscillatory integral operators in Schatten spaces, Adv. Math. 317 2017, 157 …
systems and oscillatory integral operators in Schatten spaces, Adv. Math. 317 2017, 157 …