Zobrazeno 1 - 10
of 418
pro vyhledávání: '"Nakamura, Shohei"'
The purpose of this paper is to expose and investigate natural phase-space formulations of two longstanding problems in the restriction theory of the Fourier transform. These problems, often referred to as the Stein and Mizohata--Takeuchi conjectures
Externí odkaz:
http://arxiv.org/abs/2406.14886
We reveal the relation between the Legendre transform of convex functions and heat flow evolution, and how it applies to the functional Blaschke-Santalo inequality. We also describe local maximizers in this inequality.
Externí odkaz:
http://arxiv.org/abs/2403.15357
Autor:
Nakamura, Shohei, Tsuji, Hiroshi
We prove that the functional volume product for even functions is monotone increasing along the Fokker--Planck heat flow. This in particular yields a new proof of the functional Blaschke--Santal\'{o} inequality by K. Ball and also Artstein-Avidan--Kl
Externí odkaz:
http://arxiv.org/abs/2401.00427
We establish identities for the composition $T_{k,n}(|\widehat{gd\sigma}|^2)$, where $g\mapsto \widehat{gd\sigma}$ is the Fourier extension operator associated with a general smooth $k$-dimensional submanifold of $\mathbb{R}^n$, and $T_{k,n}$ is the
Externí odkaz:
http://arxiv.org/abs/2212.12348
Autor:
Nakamura, Shohei, Tsuji, Hiroshi
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 product. More precisely, we introduce new types of hypercontractivity f
Externí odkaz:
http://arxiv.org/abs/2212.02866
In this paper, we establish local well-posedness for the Zakharov system on $\mathbb{T}^d$, $d\ge3$ in a low regularity setting. Our result improves the work of Kishimoto. Moreover, the result is sharp up to $\varepsilon$-loss of regularity when $d=3
Externí odkaz:
http://arxiv.org/abs/2212.01805
Stability of hypercontractivity, the logarithmic Sobolev inequality, and Talagrand's cost inequality
We provide deficit estimates for Nelson's hypercontractivity inequality, the logarithmic Sobolev inequality, and Talagrand's transportation cost inequality under the restriction that the inputs are semi-log-subharmonic, semi-log-convex, or semi-log-c
Externí odkaz:
http://arxiv.org/abs/2201.12478
Autor:
Bez, Neal, Nakamura, Shohei
Given any (forward) Brascamp--Lieb inequality on euclidean space, a famous theorem of Lieb guarantees that gaussian near-maximizers always exist. Recently, Barthe and Wolff used mass transportation techniques to establish a counterpart to Lieb's theo
Externí odkaz:
http://arxiv.org/abs/2110.02841
Autor:
Bennett, Jonathan, Nakamura, Shohei
We explore the extent to which the Fourier transform of an $L^p$ density supported on the sphere in $\mathbb{R}^n$ can have large mass on affine subspaces, placing particular emphasis on lines and hyperplanes. This involves establishing bounds on qua
Externí odkaz:
http://arxiv.org/abs/2001.01674
We establish new Strichartz estimates for orthonormal families of initial data in the case of the wave, Klein-Gordon and fractional Schr\"odinger equations. Our estimates extend those of Frank-Sabin in the case of the wave and Klein-Gordon equations,
Externí odkaz:
http://arxiv.org/abs/1910.03407