讲座题目: How to teach Fourier Analysis at a Technical University

讲座摘要: This talks tries to provide an executive summary of an alternative approach to Fourier Analysis prepared for graduate mathematics students or engineering students who want to understand the principles of Fourier Analysis under an application oriented perspective. This has been tested in courses at ETH Zuerich and TU Muenich (2015-2020).

Recall that Fourier Analysis is known to be important because it turns convolution into pointwise multiplication, and for engineers convolution appears in a natural way in the discussion of time-invariant linear systems (TILS) via an impulse response, or via a transfer function (multiplication operator on the Fourier transform side).

While usually the mathematical foundations of Fourier Analysis rely on the study of the Lebesgue space L^1(R^d), which is in fact a Banach algebra with respect to convolution, engineers use vague arguments to explain the above mentioned concepts. In fact, the Dirac measure is introduced as mysterious object which seems to contradict the technology of Lebesgue integration.

We will discuss some key points which allow to reconciliate the two worlds, taking at the end also a distributional viewpoint. As time permits we will also discuss the ``generalized Fourier transform for mild distributions'' which appears as a natural setting for the unified treatment of the different special variants of the Fourier transform usually treated in an engineering course: discrete and continuous, periodic and non-periodic functions.

讲座时间：2024年7月24日（周三）上午9:00

讲座方式：线下举办（综合大楼-812）

嘉宾简介：Hans Georg Feichtinger是奥地利维也纳大学数学学院（Faculty of Mathematics, University of Vienna）教授。他是国际调和分析领域，尤其是时频分析领域的著名专家。目前担任国际著名杂志Journal of Fourier Analysis and Applications的主编，同时也是一些国际期刊的副主编。Feichtinger教授在调和分析领域有着诸多建树，研究内容涉及函数空间理论，时频分析，Gabor分析和框架理论等。其中在1980年代初期，他首次引入了modulation空间，此类空间后续在调和分析与非线性偏微分方程领域取得了重要进展。Feichtinger教授目前已在顶尖期刊Transactions of the American Mathematical Society，Annales de l'Institut Henri Poincare C. Analyse Non Lineaire，Applied and Computational Harmonic Analysis，SIAM journal on mathematical analysis，Journal of Functional Analysis等上发表文章多篇。