An Introduction to the Uncertainty Principle
Hardy s Theorem on Lie Groups
(Sprache: Englisch)
In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer sity of Cambridge. One result of Wiener's visit to Cambridge was his well-known text The Fourier Integral and Certain of its Applications; another was a paper by G. H. Hardy...
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Klappentext zu „An Introduction to the Uncertainty Principle “
In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer sity of Cambridge. One result of Wiener's visit to Cambridge was his well-known text The Fourier Integral and Certain of its Applications; another was a paper by G. H. Hardy in the 1933 Journalofthe London Mathematical Society. As Hardy says in the introduction to this paper, This note originates from a remark of Prof. N. Wiener, to the effect that "a f and g [= j] cannot both be very small". ... The theo pair of transforms rems which follow give the most precise interpretation possible ofWiener's remark. Hardy's own statement of his results, lightly paraphrased, is as follows, in which f is an integrable function on the real line and f is its Fourier transform: x 2 m If f and j are both 0 (Ix1e- /2) for large x and some m, then each is a finite linear combination ofHermite functions. In particular, if f and j are x2 x 2 2 2 both O(e- / ), then f = j = Ae- / , where A is a constant; and if one x 2 2 is0(e- / ), then both are null.
Inhaltsverzeichnis zu „An Introduction to the Uncertainty Principle “
- Foreword (G. Folland)- Preface
- Euclidean Spaces
- Heisenberg Groups
- Symmetric Spaces of Rank one
- Bibliography
- Index
Bibliographische Angaben
- Autor: Sundaram Thangavelu
- 2004, Repr. d. Ausg. v. 2003., 174 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 0817643303
- ISBN-13: 9780817643300
- Erscheinungsdatum: 09.10.2003
Sprache:
Englisch
Rezension zu „An Introduction to the Uncertainty Principle “
"This nicely written book by Thangavelu is concerned with extensions of Hardy's theorem to settings that arise from noncommutative harmonic analysis.... Each chapter contains several applications to the heat equation in various settings and ends with an extensive presentation of related topics, current research, detailed references to the literature, and lists of open problems. This makes the book an invaluable resource for graduate students and researchers in harmonic analysis and applied mathematics."
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