Polar and Ol'shanskii decompositions.
Let 𝓓 be a symmetric type two Siegel domain over the cone of positive definite Hermitian matrices and let N(Φ)S be a solvable Lie group acting simply transitively on 𝓓. We characterize polynomially growing pluriharmonic functions on 𝓓 by means of three N(Φ)S-invariant second order elliptic degenerate operators.
In this paper we follow our previous research in the field of positioned agents in the eco-grammar systems and pure grammars. We extend model of the positioned eco-grammar systems by boundary markers and we introduce bordered positioned eco-grammar systems (BPEG systems, for short) and that way we show one of the possible answers to the question stated in [9]. Namely we compare generative power of the BPEG systems with three types of pure regulated grammars with appearance checking.
We show that certain quadratic base change -functions for are non-negative at their center of symmetry.
We prove that any simply connected nilpotent Lie group satisfies the qualitative uncertainty principle.
This is a collection of open problems in the theory of quantum groups. Emphasis is given to problems in the analytic aspects of the subject.