Mémoires de la Société Mathématique de France 2009; 102 pp; softcover Number: 119 ISBN10: 2856292976 ISBN13: 9782856292976 List Price: US$42 Member Price: US$33.60 Order Code: SMFMEM/119
 This volume is devoted to several generalizations of the classical Hardy uncertainty principle on Euclidean spaces. Instead of comparing functions and their Fourier transforms to a Gaussian, the author compares them to the exponential of general nondegenrate quadratic forms like the Lorentz form, for example. Using the Bargmann transform, he translates the problem into the description of several classes of analytic functions of several variables and at the same time simplifies and unifies proofs of results presented in several previous papers. A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians interested in nondegenerate quadratic forms. Table of Contents  Introduction
 Hardy's uncertainty principle and its generalizations
 Further results
 Critical and non critical pairs
 Critical pairs
 Lorentz quadratic form
 Bibliography
