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Corpus ID: 119174349

$L^q$-spectra of self-affine measures: closed forms, counterexamples, and split binomial sums

@article{Fraser2018LqspectraOS,
title={\$L^q\$-spectra of self-affine measures: closed forms, counterexamples, and split binomial sums},
author={Jonathan M. Fraser and L. Lee and I. Morris and Han Yu},
journal={arXiv: Metric Geometry},
year={2018}
}

We study $L^q$-spectra of planar self-affine measures generated by diagonal systems with an emphasis on providing closed form expressions. We answer a question posed by Fraser in 2016 in the negative by proving that a certain natural closed form expression does not generally give the $L^q$-spectrum and, using a similar approach, find counterexamples to a statement of Falconer-Miao from 2007 and a conjecture of Miao from 2008 concerning a closed form expression for the generalised dimensions of… CONTINUE READING