Memoirs of the American Mathematical Society 2001; 94 pp; softcover Volume: 153 ISBN10: 082182712X ISBN13: 9780821827123 List Price: US$51 Individual Members: US$30.60 Institutional Members: US$40.80 Order Code: MEMO/153/725
 We introduce a notion of boundary values for functions along real analytic boundaries, without any restriction on the growth of the functions. Our definition does not depend on having the functions satisfy a differential equation, but it covers the classical case of noncharacteristic boundaries. These boundary values are analytic functionals or, in the local setting, hyperfunctions. We give a characterization of nonconvex carriers of analytic functionals, in the spirit of the PaleyWienerMartineau theory for convex carriers. Our treatment gives a new approach even to the classical PaleyWiener theorem. The result applies to the study of analytic families of analytic functionals. The paper is mostly self contained. It starts with an exposition of the basic theory of analytic functionals and hyperfunctions, always using the most direct arguments that we have found. Detailed examples are discussed. Readership Graduate students and research mathematicians interested in functional analysis, several complex variables, analytic spaces, and differential equations. Table of Contents  Introduction
 Preliminaries on analytic functionals and hyperfunctions
 Appendix on good compact sets
 Analytic functionals as boundary values
 Nonlinear PaleyWiener theory
 Strong boundary values
 Strong boundary values for the solutions of certain partial differential equations
 Comparison with other notions of boundary values
 Boundary values via cousin decompositions
 The Schwarz reflection principle
 References
 Index of notions
