Quantized Canonical Transformations in Elliptic Theory

Quantized canonical transformations were introduced by Fock, Hoermander, and Maslov and play an important role in quantum mechanics and the theory of hyperbolic equations. There is a recent interest in applications of quantized canonical transformations in elliptic theory motivated by problems in Connes' noncommutative geometry and nonlocal problems in mathematical physics. This book thoroughly describes these developments.