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We characterize the equality between ultradifferentiable function classesdefined in terms of abstractly given weight matrices and in terms of thecorresponding matrix of associated weight functions by using new growthindices. These indices, defined by means of weight sequences and (associated)weight functions, are extending the notion of O-regular variation to a mixedsetting. Hence we are extending the known comparison results concerning classesdefined in terms of a single weight sequence and of a single weight functionand give also these statements an interpretation expressed in O-regularvariation.

Equality of ultradifferentiable classes by means of indices of mixed O-regular variation