Deformations of q-discrete Fock spaces: relation to q-discrete Hermite polynomials and operator- Khinchine inequality

Seminarium: 
Dyskretna analiza harmoniczna i niekomutatywna probabilistyka
Osoba referująca: 
Marek Bożejko (Uniwersytet Wrocławski)
Data: 
czwartek, 22. Luty 2024 - 10:15
Sala: 
603
Opis: 
In our talk we present the following topics:
1. (q,s)- deformations of Bozejko-Yoshida -(2006) \[ D(f) D^+(g) - sq D^+(g) D(f) = s^{N}\langle f,g\rangle \] and relations to N.Blitvic deformations.-(2012).
2. q-discrete Hermite polynomials \[ xp_{n}(x) = p_{n+1}(x) + q^{n-1}[n]_{q} p_{n-1}(x), \] relations with (q,s)-Gaussian operators.
3. Operator-Khinchine inequality for q-discrete Gaussian operators and applications.
4. Open problems.