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Uncertainty Principles Associated to Non-Degenerate Quadratic Forms
Bruno Demange, Institut Fourier, St. Martin d'Heres, France
A publication of the Société Mathématique de France.
cover
Mémoires de la Société Mathématique de France
2009; 102 pp; softcover
Number: 119
ISBN-10: 2-85629-297-6
ISBN-13: 978-2-85629-297-6
List Price: US$42
Member Price: US$33.60
Order Code: SMFMEM/119
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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
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