Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions
Abstract
We develop a theory of pseudodifferential operators of infinite order for the global classes Sω of ultradifferentiable functions in the sense of Bj\"orck, following the previous ideas given by Prangoski for ultradifferentiable classes in the sense of Komatsu. We study the composition and the transpose of such operators with symbolic calculus and provide several examples.
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