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pro vyhledávání: '"Shiraki, Shobu"'
This note is concerned with Strichartz estimates for the wave equation and orthonormal families of initial data. We provide a survey of the known results and present what seems to be a reasonable conjecture regarding the cases which have been left op
Externí odkaz:
http://arxiv.org/abs/2306.14547
We consider maximal estimates associated with fermionic systems. First we establish maximal estimates with respect to the spatial variable. These estimates are certain boundary cases of the many-body Strichartz estimates pioneered by Frank, Lewin, Li
Externí odkaz:
http://arxiv.org/abs/2306.14536
Autor:
Cho, Chu-hee, Shiraki, Shobu
We study the Hausdorff dimension of the sets on which the pointwise convergence of the solutions to the fractional Schr\"odinger equation $e^{it(-\Delta)^\frac m2}f$ fails when $m\in(0,1)$ in one spatial dimension. The pointwise convergence along a n
Externí odkaz:
http://arxiv.org/abs/2212.14330
Autor:
Cho, Chu-hee, Shiraki, Shobu
The purpose of this note is to provide a summary of the recent work of the authors on two variations of the pointwise convergence problem for the solutions to the fractional Schr\"odinger equations; convergence along a tangential line and along a set
Externí odkaz:
http://arxiv.org/abs/2212.12373
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:
Cunanan, Jayson, Shiraki, Shobu
We establish a sharp bilinear estimate for the Klein--Gordon propagator in the spirit of recent work of Beltran--Vega. Our approach is inspired by work in the setting of the wave equation due to Bez, Jeavons and Ozawa. As a consequence of our main bi
Externí odkaz:
http://arxiv.org/abs/2102.03142
Autor:
Cho, Chu-hee, Shiraki, Shobu
In this paper we study the pointwise convergence problem along a tangential curve for the fractional Schr\"odinger equations in one spatial dimension and estimate the capacitary dimension of the divergence set. We extend a prior paper by Lee and the
Externí odkaz:
http://arxiv.org/abs/2006.03272
Akademický článek
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Autor:
Aoki, Yosuke, Bennett, Jonathan, Bez, Neal, Machihara, Shuji, Matsuura, Kosuke, Shiraki, Shobu
The purpose of this article is to expose an algebraic closure property of supersolutions to certain diffusion equations. This closure property quickly gives rise to a monotone quantity which generates a hypercontractivity inequality. Our abstract arg
Externí odkaz:
http://arxiv.org/abs/1905.07911
Autor:
Shiraki, Shobu
We consider the pointwise convergence problem for the solution of Schr\"odinger-type equations along directions determined by a given compact subset of the real line. This problem contains Carleson's problem as the most simple case and was studied in
Externí odkaz:
http://arxiv.org/abs/1903.02356