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Refinement Equations and Feller Operators

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Abstract

Results on the existence and non-existence of nontrivial \({\mathbb L^1}\)-solutions of the refinement equation

$$f(x)={\int\limits_{\Omega}}|\det K(\omega)|f(K(\omega)x-L(\omega))dP(\omega)$$

are obtained by considering fixed points a Feller operator acting on measures associated with this equation.

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Authors and Affiliations

  1. Institute of Mathematics, Silesian Univeristy, Bankowa 14, 40-007, Katowice, Poland

    Janusz Morawiec & Rafał Kapica

Authors
  1. Janusz Morawiec
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  2. Rafał Kapica
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Correspondence to Janusz Morawiec.

Additional information

This research was supported by Silesian University Mathematics Department (Refinement Equations and Markov Operators program).

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Morawiec, J., Kapica, R. Refinement Equations and Feller Operators. Integr. Equ. Oper. Theory 70, 323–331 (2011). https://doi.org/10.1007/s00020-011-1879-y

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  • DOI: https://doi.org/10.1007/s00020-011-1879-y

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