Harmonic Analysis on Semi-Simple Lie Groups II
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6 Spherical Functions - The General Theory.- 6.1 Fundamentals.- 6.2 Examples.- 7 Topology on the Dual Plancherel Measure Introduction.- 7.1 Topology on the Dual.- 7.2 Plancherel Measure.- 8 Analysis on a Semi-Simple Lie Group.- 8.1 Preliminaries.- 8.2 Differential Operators on Reductive Lie Groups and Algebras.- 8.3 Central Eigendistributions on Reductive Lie Algebras and Groups.- 8.4 The Invariant Integral on a Reductive Lie Algebra.- 8.5 The Invariant Integral on a Reductive Lie Group.- 9 Spherical Functions on a Semi-Simple Lie Group.- 9.1 Asymptotic Behavior of ?-Spherical Functions on a S...
6 Spherical Functions - The General Theory.- 6.1 Fundamentals.- 6.2 Examples.- 7 Topology on the Dual Plancherel Measure Introduction.- 7.1 Topology on the Dual.- 7.2 Plancherel Measure.- 8 Analysis on a Semi-Simple Lie Group.- 8.1 Preliminaries.- 8.2 Differential Operators on Reductive Lie Groups and Algebras.- 8.3 Central Eigendistributions on Reductive Lie Algebras and Groups.- 8.4 The Invariant Integral on a Reductive Lie Algebra.- 8.5 The Invariant Integral on a Reductive Lie Group.- 9 Spherical Functions on a Semi-Simple Lie Group.- 9.1 Asymptotic Behavior of ?-Spherical Functions on a Semi-Simple Lie Group.- 9.2 Zonal Spherical Functions on a Semi-Simple Lie Group.- 9.3 Spherical Functions and Differential Equations.- 10 The Discrete Series for a Semi-Simple Lie Group - Existence and Exhaustion.- 10.1 The Role of the Distributions ?? in the Harmonic Analysis on G.- 10.2 Theory of the Discrete Series.- Epilogue.- Append.- 3 Some Results on Differential Equations.- 3.1 The Main Theorems.- 3.2 Lemmas from Analysis.- 3.3 Analytic Continuation of Solutions.- 3.4 Decent Convergence.- 3.5 Normal Sequences of is-Polynomials.- General Notational Conventions.- List of Notations.- Guide to the Literature.- Subject Index to Volumes I and II.
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