关于一类振荡积分及其在时变薛定谔方程中的应用

IF 1.2 3区 数学 Q1 MATHEMATICS
J. Behrndt , P. Schlosser
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引用次数: 0

摘要

本文将一类振荡积分解释为具有高斯正则的 Lebesgue 积分的极限。正则化积分的收敛性是通过改进版的迭代部分积分来证明的,它能产生额外的衰减因子,从而带来更好的可积分性。然后,将一般抽象结果应用于一维时间相关薛定谔方程的考奇问题,在此问题中,通过格林函数的振荡积分来表达无穷大多项式增长的 Cn 正则初始条件下的解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On a class of oscillatory integrals and their application to the time dependent Schrödinger equation
In this paper a class of oscillatory integrals is interpreted as a limit of Lebesgue integrals with Gaussian regularizers. The convergence of the regularized integrals is shown with an improved version of iterative integration by parts that generates additional decaying factors and hence leads to better integrability properties. The general abstract results are then applied to the Cauchy problem for the one dimensional time dependent Schrödinger equation, where the solution is expressed for Cn-regular initial conditions with polynomial growth at infinity via the Green's function as an oscillatory integral.
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来源期刊
CiteScore
2.50
自引率
7.70%
发文量
790
审稿时长
6 months
期刊介绍: The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.
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