5 papers
Strongly-Fibred Iterated Function Systems and the Barnsley--Vince triangle
Krzysztof Leśniak, Nina Snigireva, Filip Strobin
We review the theory of semiattractors associated with non-contractive Iterated Function Systems (IFSs) and demonstrate its applications on a concrete example. In particular, we pr…
Orthogonally Additive Sums of Powers of Linear Functionals
Christopher Boyd, Raymond Ryan, Nina Snigireva
Let be a Banach lattice, non-zero scalars and pairwise independent linear functionals on . We show that if then $\sum_{j=1}^k…
A Nakano Carrier Theorem for Polynomials
Christopher Boyd, Raymond A. Ryan, Nina Snigireva
We use a localisation technique to study orthogonally additive polynomials on Banach lattices. We derive alternative characterisations for orthogonal additivity of polynomials and…
Weakly contractive iterated function systems and beyond: A manual
Krzysztof Leśniak, Nina Snigireva, Filip Strobin
We give a systematic account of iterated function systems (IFS) of weak contractions of different types (Browder, Rakotch, topological). We show that the existence of attractors an…
Geometry of Spaces of Orthogonally Additive Polynomials on C(K)
Christopher Boyd, Raymond A. Ryan, Nina Snigireva
We study the space of orthogonally additive -homogeneous polynomials on . There are two natural norms on this space. First, there is the usual supremum norm of uniform con…