Abstract
In this paper, we derive explicit expressions for some classes of *- moments of a free unitary Brownian motion compressed by a free projection, using various methods. While the moments of this nonnormal operator are readily derived through analytical or combinatorial methods, we only succeeded to derive its mixed ones after solving a nonlinear partial differential equation (pde) for their generating function. We shall also give some interest in odd alternating moments. In particular, we derive a linear pde for their generating function which we solve when the rank of the projection equals 1/2.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 413-433 |
| Number of pages | 21 |
| Journal | Journal of Operator Theory |
| Volume | 87 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2022 |
Keywords
- Alternating moments
- Free unitary brownian motion
- Kreweras complement
- Mixed moments
- Noncrossing partitions
- Selfadjoint projection
ASJC Scopus subject areas
- Algebra and Number Theory