Title：From Fourier Analysis to Gaussian Measures

Speaker：徐佩（美国西北大学，中国科学技术大学）

Time：2017年10月30日    下午4:00--5:30

Room：东区管理科研楼   数学科学学院1318室

Abstract： AGaussian function is the exponential of a quadratic complex function whoseleading coefficient is real negative. Starting from the fact that the class ofGaussian functions is invariant under Fourier transform we will discuss manywell known and not so well known wonderful properties of Gaussian measures,including Stein/'92s characterization and the correlation dominationinequality.  We will show the specialrole of the Ornstein-Uhlenbeck operator (classical harmonic oscillator inquantum mechanics) and discuss its spectral property and the generalizedspectral gap theorem. We will discuss the classical Poincare inequality and thelogarithmic Sobolev inequality for the Gaussian measure and show that they arespecial cases of Beckner/'92s inequality. The prerequisite of the talk is agood knowledge of niversity calculus. The talk promises to be elementary andentertaining and students and mathematicians at all levels and in all fieldsare welcome.