Nilpotent operators and weighted projective lines

Weighted Projective Spaces and Minimal Nilpotent Orbits

We investigate (twisted) rings of differential operators on the resolution of singularities of an irreducible component X of Omin ∩ n+ (where Omin is the (Zariski) closure of the minimal nilpotent orbit of sp2n and n+ is the Borel subalgebra of sp2n) using toric geometry, and show that they are homomorphic images of a certain family of associative subalgebras of U(sp2n), which contains the maxi...

Weighted Frobenius-Perron and Koopman operators

Linear and projective boundary of nilpotent groups

We define a pseudometric on the set of all unbounded subsets of a metric space. The Kolmogorov quotient of this pseudometric space is a complete metric space. The definition of the pseudometric is guided by the principle that two unbounded subsets have distance 0 whenever they stay sublinearly close. Based on this pseudometric we introduce and study a general concept of boundaries of metric spa...

Weighted slant Toep-Hank Operators

A $it{weighted~slant~Toep}$-$it{Hank}$ operator $L_{phi}^{beta}$ with symbol $phiin L^{infty}(beta)$ is an operator on $L^2(beta)$ whose representing matrix consists of all even (odd) columns from a weighted slant Hankel (slant weighted Toeplitz) matrix, $beta={beta_n}_{nin mathbb{Z}}$ be a sequence of positive numbers with $beta_0=1$. A matrix characterization for an operator to be $it{weighte...

Equivalence operators in nilpotent systems