Foundations of Algebraic Analysis (PMS-37), Volume 37 / Princeton Mathematical Series (PDF)

The use of algebraic methods for studying analysts is an important theme in modern mathematics. The most significant development in this field is microlocal analysis, that is, the local study of differential equations on cotangent bundles. This treatise provides a thorough description of microlocal analysis starting from its foundations. The book begins with the definition of a hyperfunction. It then carefully develops the microfunction theory and its applications to differential equations and theoretical physics. It also provides a description of microdifferential equations, the microlocalization of linear differential equations. Finally, the authors present the structure theorems for systems of microdifferential equations, where the quantized contact transformations are used as a fundamental device.

The microfunction theory, together with the quantized contact transformation theory, constitutes a valuable new viewpoint in linear partial differential equations.

Originally published in 1986.

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