Author | Thangavelu, Sundaram. author |
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Title | An Introduction to the Uncertainty Principle [electronic resource] : Hardy's Theorem on Lie Groups / by Sundaram Thangavelu |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2004 |
Connect to | http://dx.doi.org/10.1007/978-0-8176-8164-7 |
Descript | XIII, 174 p. online resource |
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