Harmonic Analysis on Semi-Simple Lie Groups II [Paperback]

6 Spherical Functions  The General Theory.- 6.1 Fundamentals.- 6.1.1 Spherical Functions  Functional Properties.- 6.1.2 Spherical Functions  Differential Properties.- 6.2 Examples.- 6.2.1 Spherical Functions on Motion Groups.- 6.2.2 Spherical Functions on Semi-Simple Lie Groups.- 7 Topology on the Dual Plancherel Measure Introduction.- 7.1 Topology on the Dual.- 7.1.1 Generalities.- 7.1.2 Applications to Semi-Simple Lie Groups.- 7.2 Plancherel Measure.- 7.2.1 Generalities.- 7.2.2 The Plancherel Theorem for Complex Connected Semi-Simple Lie Groups.- 8 Analysis on a Semi-Simple Lie Group.- 8.1 Preliminaries.- 8.1.1 Acceptable Groups.- 8.1.2 Normalization of Invariant Measures.- 8.1.3 Integration Formulas.- 8.1.4 A Theorem of Compacity.- 8.1.5 The Standard Semi-Norm on a Semi-Simple Lie Group.- 8.1.6 Completely Invariant Sets.- 8.2 Differential Operators on Reductive Lie Groups and Algebras.- 8.2.1 Radial Components of Differential Operators on a Manifold.- 8.2.2 Radial Components of Polynomial Differential Operators on a Reductive Lie Algebra.- 8.2.3 Radial Components of Left Invariant Differential Operators on a Reductive Lie Group.- 8.2.4 The Connection between Differential Operators in the Algebra and on the Group.- 8.3 Central Eigendistributions on Reductive Lie Algebras and Groups.- 8.3.1 The Main Theorem in the Algebra.- 8.3.2 Properties of FT-I.- 8.3.3 The Main Theorem on the Group.- 8.3.4 Properties of FT- II.- 8.3.5 Rapidly Decreasing Functions on a Euclidean Space.- 8.3.6 Tempered Distributions on a Reductive Lie Algebra.- 8.3.7 Rapidly Decreasing Functions on a Reductive Lie Group.- 8.3.8 Tempered Distributions on a Reductive Lie Group.- 8.3.9 Tools for Harmonic Analysis on G.- 8.4 The Invariant Integral on a Reductive Lie Algebra.- 8.4.1 The Invariant Integral  Definition and Properties.- 8.4.2 Computations in sl(2, R).- 8.4.3 Continuity of the Map f ? ?f.- 8.4.4 Extension Problems.- 8.4.5 The Main Theorem.- 8.5 The Invariant Integral on a Reductive Liló¾