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We develop a theory of pseudodifferential operators of infinite order for theglobal classes $\mathcal{S}_{\omega}$ of ultradifferentiable functions in thesense of Bj\"orck, following the previous ideas given by Prangoski forultradifferentiable classes in the sense of Komatsu. We study the compositionand the transpose of such operators with symbolic calculus and provide severalexamples.

Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions