If you were unable to attend, you may view Dr. Alpay’s lecture slides here.
Schmid College is excited to announce that next week, Professor Daniel Alpay will be on campus giving a lecture series. Alpay is very influential in the field of Complex Analysis and is the Earl Katz Chair in Algebraic System Theory, Department of Mathematics, at Ben-Gurion University of the Negev.
The title of his lecture series is “Infinite dimensional analysis, non commutative stochastic, distributions and applications” and all his talks will be held in
Von Neumann Hall
, located at 545 West Palm Ave. Please mark your calendar for these lectures and join us!
Tuesday, February 10 | 10:00 a.m. to noon
Lecture 1: Positive definite functions, Countably normed spaces, their duals and Gelfand triples
We survey the notion of positive definite functions and of the associated reproducing kernel Hilbert spaces. Examples are given relevant to the sequel of the talks. We also define nuclear spaces and Gelfand triples, and give as examples Schwartz functions and tempered distributions.
Thursday, February 12 | 11:00 a.m. to 1:00 p.m.
Lecture 2: Bochner and Bochner-Minlos theorem. Hida’s white noise space and Kondratiev’s spaces of stochastic distributions, Stationary increments stochastic processes. Linear stochastic systems.
We discuss the Bochner-Minlos theorem and build Hida’s white noise space. We build stochastic processes in this space with derivative in the Kondratiev space of stochastic distributions. This space is an algebra with the Wick product, and its structure of tallows to define stochastic integrals.
Friday, February 13, 10:00 a.m. to noon
Lecture 3: Fock spaces and non commutative stochastic distributions | The free setting. Free (non commutative) stochastic processes.
We present the non commutative counterpart of the previous talk. We will review the main definitions of free analysis required and then present, and build stationary increments non commutative processes.
The values of their derivatives are now continuous operators from the space of non commutative stochastic test functions into the space of non commutative stochastic distributions.