Cyclicity in EL–Hypergroups

CYCLICITY OF (Z/(p))×

Cyclicity versus Center Problem

We prove that there are one-parameter families of planar differential equations for which the center problem has a trivial solution and on the other hand the cyclicity of the weak focus is arbitrarily high. We illustrate this phenomenon in several examples for which this cyclicity is computed.

Cyclicity of graphs

The cyclicity of a graph is the largest integer n for which the graph is contractible to the cycle on n vertices. By analyzing the cycle space of a graph, we establish upper and lower bounds on cyclicity. These bounds facilitate the computation of cyclicity for several classes of graphs, including chordal graphs, complete n-partite graphs, n-cubes, products of trees and cycles, and planar graph...

Cyclicity in Rank-one Perturbation Problems

The property of cyclicity of a linear operator, or equivalently the property of simplicity of its spectrum, is an important spectral characteristic that appears in many problems of functional analysis and applications to mathematical physics. In this paper we study cyclicity in the context of rank-one perturbation problems for self-adjoint and unitary operators. We show that for a fixed non-zer...

On Cyclicity in Weighted Dirichlet Spaces

We extend some results of Brown and Shields on cyclicity to weighted Dirichlet spaces 0<α< 1. We prove a comparison theorem for cyclicity in these spaces and provide a result on the geometry of the family of cyclic vectors in general functional Hilbert spaces.