Infinite dimensional oscillatory integrals as projective systems of functionals

Sergio Albeverio; Sonia Mazzucchi

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Infinite dimensional oscillatory integrals as projective systems of functionals

机译：无限维振荡积分作为泛函的射影系统

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摘要

The theory of infinite dimensional oscillatory integrals and some of its applications are discussed, with special attention to the relations with the original work of K. Ito in this area. A recent general approach to infinite dimensional integration which unifies the case of oscillatory integrals and the case of probabilistic type integrals is presented, together with some new developments.

机译：讨论了无限维振荡积分的理论及其一些应用，特别注意与K. Ito在该领域的原始工作的关系。提出了一种最新的无穷维积分通用方法，该方法统一了振荡积分和概率类型积分的情况，以及一些新的发展。

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来源
《Journal of the Mathematical Society of Japan》 |2015年第4期|1295-1316|共22页
作者
Sergio Albeverio; Sonia Mazzucchi;
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作者单位

Institut fuEr Angewandte Mathematik and HCM IZKS, UniversitaEt Bonn Endenicher Allee 60 53115 Bonn BIBOS Cerfim (Locarno) Germany;

Dipartimento di Matematica Universita di Trento via Sommarive 14 I-38123 Trento Italy;

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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
integration theory via linear continuous functionals; measure theory on infinite dimensional spaces; Feynman path integrals;

机译：通过线性连续函数的积分理论;在无穷维空间上的测度理论;费曼路径积分;

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1. Infinite Dimensional Oscillatory Integrals with Polynomial Phase and Applications to Higher-Order Heat-Type Equations [J] . Mazzucchi S. Potential analysis: An international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis . 2018,第2期

机译：具有多项式阶段的无限尺寸振荡积分和高阶热型方程的应用
2. Equilibria trajectories as stationary solutions of infinite-dimensional projected dynamical systems [J] . Raciti F. Applied mathematics letters . 2004,第2期

机译：平衡轨迹作为无穷维投影动力学系统的平稳解
3. Symplectic geometry on an infinite-dimensional phase space and an asymptotic representation of quantum averages by Gaussian functional integrals [J] . A. Yu. Khrennikov Izvestiya. Mathematics . 2008,第1期

机译：无限维相空间上的辛几何和量子平均的高斯泛函渐近表示
4. Integral input-to-state stability of bilinear infinite-dimensional systems [C] . Mironchenko Andrii, Ito Hiroshi IEEE Annual Conference on Decision and Control . 2014

机译：双线性无穷维系统的输入到状态积分稳定性
5. Infinite-dimensional dynamical systems and projections. [D] . Ott, William. 2004

机译：无限维动力系统和投影。
6. Predicting chaos for infinite dimensional dynamical systems: the Kuramoto-Sivashinsky equation a case study. [O] . Y S Smyrlis, D T Papageorgiou 1991

机译：预测无穷维动力学系统的混沌：Kuramoto-Sivashinsky方程一个案例研究。
7. Finite Dimensional Approximation Approach to Oscillatory Integrals and Stationary Phase in Infinite Dimensions [O] . Albeverio S., Brzezniak Z. 1993

机译：无限维振荡积分和平稳相的有限维近似方法
8. Instability of Nonlinear Infinite-Dimensional Feedback Systems Using Lyapunov Functionals. [R] . Steding, T., Bergen, A. 1971

机译：基于Lyapunov泛函的非线性无限反馈系统的不稳定性。

Infinite dimensional oscillatory integrals as projective systems of functionals

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