## Abstract

We consider $L^q$-spectra of planar graph-directed self-affine measures generated by diagonal or anti-diagonal matrices. Assuming the directed graph is strongly connected and the system satisfies the rectangular open set condition, we obtain a general closed form expression for the $L^q$-spectra. Consequently, we obtain a closed form expression for box dimensions of associated planar graph-directed box-like self-affine sets. We also provide a precise answer to a question of Fraser in 2016 concerning the $L^q$-spectra of planar self-affine measures generated by diagonal matrices.

## Full Text

### Topics from this Paper

- Diagonal Matrices
- Spectra Of Measures
- Open Condition
- Open Set Condition
- Self-affine Measures + Show 5 more

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