Author | Thangavelu, Sundaram. author |
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Title | Harmonic Analysis on the Heisenberg Group [electronic resource] / by Sundaram Thangavelu |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1998 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1772-5 |
Descript | XII, 195 p. online resource |
1 The Group Fourier Transform -- 1.1 The Heisenberg group -- 1.2 The Schrรถdinger representations -- 1.3 The Fourier and Weyl transforms -- 1.4 Hermite and special Hermite functions -- 1.5 PaleyโWiener theorems for the Fourier transform -- 1.6 An uncertainty principle on the Heisenberg group -- 1.7 Notes and references -- 2 Analysis of the Sublaplacian -- 2.1 Spectral theory of the sublaplacian -- 2.2 Spectral decomposition for Lp functions -- 2.3 Restriction theorems for the spectral projections -- 2.4 A Paley-Wiener theorem for the spectral projections -- 2.5 Bochner-Riesz means for the sublaplacian -- 2.6 A multiplier theorem for the Fourier transform -- 2.7 Notes and references -- 3 Group Algebras and Applications -- 3.1 The Heisenberg motion group -- 3.2 Gelfand pairs, spherical functions and group algebras -- 3.3 An algebra of radial measures -- 3.4 Analogues of Wiener-Tauberian theorem -- 3.5 Spherical means on the Heisenberg group -- 3.6 A maximal theorem for spherical means -- 3.7 Notes and references -- 4 The Reduced Heisenberg Group -- 4.1 The reduced Heisenberg group -- 4.2 A Wiener-Tauberian theorem for Lp functions -- 4.3 A maximal theorem for spherical means -- 4.4 Mean periodic functions on phase space -- 4.5 Notes and references