Abstract
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.
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Translated from Itogi Nauk i Tekhniki, Sovremennye Problemy Matematiki, Vol. 13, pp. 5–144, 1979.
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Maslov, V.P., Nazaikinskii, V.E. Algebras with general commutation relations and their applications. I. Pseudodifferential equations with increasing coefficients. J Math Sci 15, 167–273 (1981). https://doi.org/10.1007/BF01083678
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DOI: https://doi.org/10.1007/BF01083678