Zobrazeno 1 - 10
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pro vyhledávání: '"Taira, Kouichi"'
Autor:
Taira, Kouichi
A local time decay estimate of fractional Schr\"odinger operators with slowly decaying positive potentials are studied. It is shown that its resolvent is smooth near zero and the time propagator has fast local time decay which is very different from
Externí odkaz:
http://arxiv.org/abs/2403.16148
Autor:
Taira, Kouichi, Tamori, Hiroyoshi
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}rsted, and for the operators $|x|^{2-a}\Delta_k$. Here $k$ denotes a n
Externí odkaz:
http://arxiv.org/abs/2308.16815
Autor:
Taira, Kouichi
In this short note, smoothness of the fundamental solution of Schr\"odinger equations on a complete manifold is studied. It is shown that (1) the fundamental solution is smooth under "mild" trapping conditions; (2) there is a Riemannian manifold whic
Externí odkaz:
http://arxiv.org/abs/2203.01499
Autor:
Nakamura, Shu, Taira, Kouichi
Let $X=\mathbb{R}\times M$ be the spacetime, where $M$ is a closed manifold equipped with a Riemannian metric $g$, and we consider a symmetric Klein-Gordon type operator $P$ on $X$, which is asymptotically converges to $\partial_t^2-\triangle_g$ as $
Externí odkaz:
http://arxiv.org/abs/2203.00178
Autor:
Nakamura, Shu, Taira, Kouichi
Here we discuss a new simplified proof of the essential self-adjointness for formally self-adjoint differential operators of real principal type, previously proved by Vasy (2020) and Nakamura-Taira (2021). For simplicity, here we discuss the second o
Externí odkaz:
http://arxiv.org/abs/2202.13499
Autor:
Taira, Kouichi
In this short note, we prove Strichartz estimates for Schr\"odinger operators with slowly decaying singular potentials in dimension two. This is a generalization of the recent results by Mizutani, which are stated for dimension greater than two. The
Externí odkaz:
http://arxiv.org/abs/2108.02900
Autor:
Taira, Kouichi
In this note, we study a geometric property of asymptotically Minkowski spacetimes and an analytic property of the Klein-Gordon operator. Precisely, our first main results show that asymptotically Minkowski spacetimes are geodesically complete under
Externí odkaz:
http://arxiv.org/abs/2107.10509
Autor:
Taira, Kouichi
In this paper, we shall show that the limiting absorption principle for the wave operator on the asymptotically Minkowski spacetime. This problem was previously considered by [A. Vasy, J. Spect. Theory, 10,439-461 , (2020)]. Here, we employ a more tr
Externí odkaz:
http://arxiv.org/abs/2012.07946
Autor:
Taira, Kouichi
In this note, we prove the uniform resolvent estimate of the discrete Schr\"odinger operator with dimension three. To do this, we show a Fourier decay of the surface measure on the Fermi surface.
Comment: 19pages
Comment: 19pages
Externí odkaz:
http://arxiv.org/abs/2005.09366
Autor:
Taira, Kouichi
In this article, we prove that the completeness of the Hamilton flow and essential self-adjointness are equivalent for real principal type operators on the circle. Moreover, we study spectral properties of these operators. The proof is based on the c
Externí odkaz:
http://arxiv.org/abs/2004.07547