Poisson Integrals and Boundary Components of Symmetric Spaces.
We give a construction of a Poisson transform mapping density valued differential forms on generalized flag manifolds to differential forms on the corresponding Riemannian symmetric spaces, which can be described entirely in terms of finite dimensional representations of reductive Lie groups. Moreover, we will explicitly generate a family of degree-preserving Poisson transforms whose restriction to real valued differential forms has coclosed images. In addition, as a transform on sections of density...
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.