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Operators of the regular representation for commutation relations of general form are constructed. On the basis of the technique developed, conditions for the existence of a mixed (with respect to smoothness and rate of growth at infinity) asymptotic expression for a solution of a pseudodifferential equation with increasing coefficients are obtained. The work contains a survey of the general theory of quasiinversion of functions of ordered operators.

Algebras with general commutation relations and their applications. I. Pseudodifferential equations with increasing coefficients