Annoucements • Office = MATH 221 (Directly above the Mathematics Department Office.) • Email = [email protected] • Text = “Baby Rudin” – Principles of Mathematical Analysis 3/e by Walter Rudin • Course Website = “http://www.math.ubc.ca/∼feldman/m321/” • Topics: – Riemann-Stieltjes integral (§6) – Sequences & Series of functions (§7) – Power Series, Special Functions, Fourier Series (§8) – Ano...

Let H be a separable infinite-dimensional Hubert space over R. The Fresnel class T(H) of H consists of all Fourier-Stieltjes transforms of bounded Borel measures on H. There are several results insuring that various functions of interest in connection with the Feynman integral and quantum mechanics are in 7{H). We give a theorem which has most of these results as corollaries as well as many fur...

We provide complete characterizations, on Banach spaces with cotype 2, of those linear operators which happen to be weakly mixing or strongly mixing transformations with respect to some nondegenerate Gaussian measure. These characterizations involve two families of small subsets of the circle: the countable sets, and the so-called sets of uniqueness for Fourier-Stieltjes series. The most intere...