3 papers
math.SP2025
On the dimension of orbits of matrix pencils under strict equivalence
Fernando De Terán, Froilán M. Dopico, Patryk Pagacz
We prove that, given two matrix pencils and , if belongs to the closure of the orbit of under strict equivalence, then the dimension of the orbit of is smaller t…
math.SP2024
The Taylor spectrum of pairs of isometries
Zbigniew Burdak, Patryk Pagacz
In the paper we fully describe Taylor spectrum of pairs of isometries given by diagrams. In most cases both isometries in such pairs have non-trivial shift part and its Taylor spec…
math.PR2024
An operator theory approach to the evanescent part of a two-parametric weak-stationary stochastic process
Zbigniew Burdak, Marek Kosiek, Patryk Pagacz +1
A new approach to the evanescent part of a two-dimensional weak-stationary stochastic process with the past given by a half-plane is proceed. The classical result due to Helson and…