On the quantization of rapidly oscillating symbols

The authors construct a calculus of functions of coordinate and differentiation operators, ordered in an arbitrary manner. The transition from one order to another is studied, and it is shown that linear combinations of functions of this form with exponential oscillating symbols yield global asymptotic solutions of pseudodifferential equations with smooth bicharacteristics. Formulas are obtained for the composition of two operators with oscillating symbols.
Bibliography: 22 titles.