Complex Analysis and Operator Theory

, Volume 12, Issue 4, pp 1015–1026 | Cite as

Dynamics of Orthonormal Bases Associated to Basins of Attraction

  • James Tipton


Alpay et al. (in: Recent advances in inverse scattering, Schur analysis, and stochastic processes, Springer, Berlin, pp 67–87, 2015), a technique was developed which allows for the construction of a reproducing kernel Hilbert space on basins of attraction containing 0. When the right conditions are met, an explicit orthonormal basis can be constructed using a particular class of operators. It is natural then to consider how the orthonormal basis changes as we let the basin of attraction vary. We will consider this question for the basins of attraction containing 0 of the family of polynomials \(\mathcal {F} = \{az^{2^{n+2}}-2az^{2^{n+1}}:a\ne 0\}\), where \(n\in \mathbb {N}\).


Infinite products Cuntz algebras Dynamical systems Julia sets 

Mathematics Subject Classification

Primary 40A20 47B32 Secondary 37F50 


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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Department of Mathematical Sciences, 101 Mathematics BuildingUniversity of MontanaMissoulaUSA

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