An Introduction to the Uncertainty Principle Hardy’s Theorem on Lie Groups
Motivating this interesting monograph is the development of a number of analogs of Hardy's theorem in settings arising from noncommutative harmonic analysis. This is the central theme of this work. Specifically, it is devoted to connections among various theories arising from abstract harmonic...
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| Format: | eBook |
| Language: | English |
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Boston, MA
Birkhäuser Boston
2004, 2004
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| Edition: | 1st ed. 2004 |
| Series: | Progress in Mathematics
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| Subjects: | |
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| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1 Euclidean Spaces
- 1.1 Fourier transform on L1(?n)
- 1.2 Hermite functions and L2 theory
- 1.3 Spherical harmonics and symmetry properties
- 1.4 Hardy’s theorem on ?n
- 1.5 Beurling’s theorem and its consequences
- 1.6 Further results and open problems
- 2 Heisenberg Groups
- 2.1 Heisenberg group and its representations
- 2.2 Fourier transform on Hn
- 2.3 Special Hermite functions
- 2.4 Fourier transform of radial functions
- 2.5 Unitary group and spherical harmonics
- 2.6 Spherical harmonics and the Weyl transform
- 2.7 Weyl correspondence of polynomials
- 2.8 Heat kernel for the sublaplacian
- 2.9 Hardy’s theorem for the Heisenberg group
- 2.10 Further results and open problems
- 3 Symmetric Spaces of Rank 1
- 3.1 A Riemannian space associated to Hn
- 3.2 The algebra of radial functions on S
- 3.3 Spherical Fourier transform
- 3.4 Helgason Fourier transform
- 3.5 Hecke-Bochner formula for the Helgason Fourier transform
- 3.6 Jacobi transforms
- 3.7 Estimating the heat kernel
- 3.8 Hardy’s theorem for the Helgason Fourier transform
- 3.9 Further results and open problems