7 citations · 13 across the 7 of their papers we have counts for
10 papers
Hypercontractivity beyond Nelson's time and its applications to Blaschke--Santaló inequality and inverse Santaló inequality
Shohei Nakamura, Hiroshi Tsuji
We explore an interplay between an analysis of diffusion flows such as Ornstein--Uhlenbeck flow and Fokker--Planck flow and inequalities from convex geometry regarding the volume p…
Tomography bounds for the Fourier extension operator and applications
Jonathan Bennett, Shohei Nakamura
We explore the extent to which the Fourier transform of an density supported on the sphere in can have large mass on affine subspaces, placing particular empha…
Strichartz estimates for orthonormal families of initial data and weighted oscillatory integral estimates
Neal Bez, Sanghyuk Lee, Shohei Nakamura
We establish new Strichartz estimates for orthonormal families of initial data in the case of the wave, Klein-Gordon and fractional Schrödinger equations. Our estimates extend thos…
Maximal estimates for the Schrödinger equation with orthonormal initial data
Neal Bez, Sanghyuk Lee, Shohei Nakamura
For the one-dimensional Schrödinger equation, we obtain sharp maximal-in-time and maximal-in-space estimates for systems of orthonormal initial data. The maximal-in-time estimates…
Finite difference scheme for two-dimensional periodic nonlinear Schrödinger equations
Younghun Hong, Chulkwang Kwak, Shohei Nakamura +1
A nonlinear Schrödinger equation (NLS) on a periodic box can be discretized as a discrete nonlinear Schrödinger equation (DNLS) on a periodic cubic lattice, which is a system of fi…
The orthonormal Strichartz inequality on torus
Shohei Nakamura
In this paper, motivated by recent important works due to Frank-Lewin-Lieb-Seiringer \cite{FLLS} and Frank-Sabin \cite{frank-sabin-1}, we study the Strichartz inequality on torus w…