LIE'S THEOREMS FOR GENERALISED TRANSLATION OPERATORS

CONTENTS Introduction § 1. The group ring § 2. A generalisation of the group ring and generalised translation operators § 3. Definition of infinitesimal operators and Lie's first theorem for generalised translation operators § 4. Lie's second and third theorems for generalised translation operators. The case of first-order infinitesimal operators § 5. Lie's second and third theorems for generalised translation operators. The case of second-order operators § 6. The converse of Lie's first theorem for generalised translation operators § 7. A description of the class § 8. The converse of Lie's second theorem for generalised translation operators § 9. The converse of Lie's third theorem for generalised translation operators § 10. The construction of the operators , which commute with the operators § 11. Canonical operators § 12. Transformation operators § 13. Some questions of convergence § 14. Finite-dimensional subspaces invariant under infinitesimal operators (an analogue of representation theory for generalised translation operators) § 15. Examples References