Based on a seminar sponsored by the Institute for Advanced Study in 1977-1978, this set of papers introduces micro-local analysis concisely and clearly to mathematicians with an analytical background. The papers treat the theory of microfunctions and applications such as boundary values of elliptic partial differential equations, propagation of singularities in the vicinity of degenerate characteristics, holonomic systems, Feynman integrals from the hyperfunction point of view, and harmonic analysis on Lie groups.

Victor Guillemin, Masaki Kashiwara & Takahiro Kawai

• Frontmatter,
• TABLE OF CONTENTS,
• PREFACE,
• INTRODUCTION TO THE THEORY OF HYPERFUNCTIONS,
• SOME APPLICATIONS OF BOUNDARY VALUE PROBLEMS FOR ELLIPTIC SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS,
• A SZEGO-TYPE THEOREM FOR SYMMETRIC SPACES,
• SOME MICRO-LOCAL ASPECTS OF ANALYSIS ON COMPACT SYMMETRIC SPACES,
• ON HOLONOMIC SYSTEMS WITH REGULAR SINGULARITIES,
• MICRO-LOCAL ANALYSIS OF FEYNMAN AMPLITUDES,
• Backmatter,