Quantization Methods in the Theory of Differential Equations

This volume presents a systematic and mathematically rigorous exposition of methods for studying linear partial differential equations. It focuses on quantization of the corresponding objects (states, observables, and canonical transformations) in the phase space. The quantization of all three types of classical objects is carried out in a unified way with the use of a special integral transform. This book covers recent as well as established results, all treated within the framework of a universal approach. It also includes applications and provides a useful reference text for graduate and research-level readers.