The theme of this volume is a treatment of differential equations on a \(C^\infty\) manifold \(V\) by separation of variables techniques. More specifically, given a Lie transformation group \(L\) of \(V\) and a Lie subgroup \(H\subset L\), if \(D(V)\) is the set of differential operators on \(V\) invariant under \(L\), then the principal object of study is the set of distributions \(T\) on \(V\) satisfying the following two conditions:(i) \(T\) is an eigendistribution of each \(D\in D(V)\); (ii) \(T\) is invariant under \(H\).

Readership

Reviews

"The results in these notes are mainly due to Harish-Chandra and the author. The common point of view in the treatment of these ... important examples is very interesting."

-- E. Thoma, Mathematical Reviews

Table of Contents

• Introduction
• Some geometric properties of differential operators
• Spherical functions on symmetric spaces
• Conical distributions on the space of horocycles
• Central eigendistributions and characters
• Bibliography