Dispersive estimates and asymptotic expansions for Schroedinger equations in dimension one

Haruya Mizutani

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Dispersive estimates and asymptotic expansions for Schroedinger equations in dimension one

机译：一维Schroedinger方程的色散估计和渐近展开

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We study the time decay of scattering solutions to onedimensional Schroedinger equations and prove a weighted dispersive estimate with stronger time decay than the case of unweighted estimates for the nonresonant state. Furthermore asymptotic expansions in time of scattering solutions are given. The key of the proof is the study of the Fourier properties of the Jost functions. We improve the Fourier properties of the Jost functions obtained by D'Ancona and Fanelli [2].

机译：我们研究了一维Schroedinger方程的散射解的时间衰减，并证明了与非共振状态的非加权估计相比，加权色散估计具有更强的时间衰减。此外，给出了散射解的时间渐近扩展。证明的关键是对Jost函数的傅里叶特性的研究。我们改善了D'Ancona和Fanelli [2]获得的Jost函数的傅立叶特性。

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来源
《Journal of the Mathematical Society of Japan》 |2011年第1期|p.239-261|共23页
作者
Haruya Mizutani;
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作者单位

Graduate School of Mathematical Sciences University of Tokyo 3-8-1 Komaba, Meguro-ku Tokyo 153-8914, Japan;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
dispersive estimate; asymptotic expansion; schrodinger equation;

机译：分散估计渐近展开薛定inger方程;

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2. Dispersive estimates of solutions to the Schroedinger equation in dimensions n ≥ 4 [J] . Georgi Vodev Asymptotic analysis . 2006,第1a2期

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3. Asymptotic expansions of canards with poles. Application to the stationary unidimensional Schroedinger equation [J] . Benoit E. Zeitschrift fur Angewandte Mathematik und Mechanik . 1996,第S2期

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4. Numerical Solution of the two-dimensional time independent Schroedinger Equation by symplectic schemes based on Magnus Expansion [C] . Z. Kalogiratou, Th. Monovasilis, T.E. Simos Advances in Computational Methods in Sciences and Engineering 2005 vol.4A; Lecture Series on Computer and Computational Sciences; vol.4A . 2005

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8. Asymptotics of the Nodal Lines of Solutions of 2-Dimensional Schroedinger Equations [R] . Hoffmann-Ostenhof, M. 1987

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Dispersive estimates and asymptotic expansions for Schroedinger equations in dimension one

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