## A relationship between harmonic analysis on SU(2) and on SL(2,C)/SU(2) |

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### Contents

The Abelian Poisson Summation Formula | 9 |

The Structure of SL2C | 32 |

A Review of Harmonic Analysis on SL2C | 67 |

3 other sections not shown

### Common terms and phrases

abelian bi-invariant bump function Cartan decomposition Cartan subgroup chapter character compact computation construct convergence coordinate chart corresponding defined denote dense open submanifold diffeomorphism differential dimensional dkM dn dual group equivalence of homogeneous equivariant Euler angle Euler angle map example exponential map fact factor finite Fourier coefficients Fourier transform functions on G G action G/HxH Haar measure Harish-Chandra harmonic analysis Helgason 16 homogeneous space invariant measure inversion isomorphism Iwasawa left invariant Lie algebra Lie group manifold structure matrix elements noncompact numbers obtained orthonormal basis overlap maps parameter Poisson summation formula projection proof quotient representations restricted rotation Schwartz function Schwartz space semisimple shows smooth functions sphere spherical functions spiral submanifolds subsection subspace tangent space tempered distributions test functions Theorem tion topological unitary vector space volume form Wallach 36 Warner 38 Weyl covering Weyl integral formula