Abstract
We propose constructions of multiparameter depending scales of Banach spaces of anisotropic ultra-differentiable functions and investigate their invariance under changes of the variables. We prove new local solvability results in such spaces for some classes of linear and semilinear partial differential equations with multiple characteristics.
Acknowledgements
The authors thank Stevan Pilipović and Petar Popivanov for useful discussions on the subject of the paper.