Differential Operators on Manifolds: Lectures given at a Summer School of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Varenna ... 2, 1975 (C.I.M.E. Summer Schools, 70)

Cover
Differential Operators on Manifolds
ISBN 9783642111136
Contents
Classical Groups and Classical Differentjal Operators on Manifolds
	Lecture I
		Introduction
		1. The Exterior Algebra
		2. Characters
	Lecture II
		Introduction
		1. The Clifford algebra
	Lecture III
		Introduction
		1. The Hodge - de Rham theory
		2 . The Euler characteristic and signature
	Lecture IV
		Introduction
		1. The Dirac operator
		2. The Image-operator
		3. Relation of Image and the Dirac operator
	Lecture V
		Introduction
		1. The Bott periodicity theorem
		2. K-theory
	Lecture VI
		Introduction
		1. Structure of the prpof
		2. Construction of alpha
	Lecture VII
		Introduction
		1. The heat equation formula
		2. Application of invariance theory
	Lecture VIII
		Introduction
		1. The generalized Signature operator
		2. Lefschetz formula
	References
Some Aspects of Invariant Theory in Differential Geometry
	1. Introduction
	2. Some basic theorems in differential geometry
	3. The full linear group
	4. The Group Diff M
	5. The Jet-spaces Image
	6. The natural thickenings of M
	7. The first main theorem of invariant theory and some of its applications
	8. Characteristic classes of Foliations
	Bibliography
Singular Integral Operators and Nilpotent Groups
	1. The Hilbert transform and the Cauchy integral
	2. Homogeneous distributions in Image
	3. LP Theory
	4. Sobolev and Lipschitz spaces
	5. Pseudo-differential operators
	6. Parametricies and estimates for elliptic operators
	7. Entr\'acte
	8. Cauchy-Szego integral and Heisenberg group
	9. Homogeneous groups
	10. The Image-complex on the Heisenberg group
	11. The Lewy equation
	12. Application to hypoelliptic operators Literature
	Literature
Diffusions et Geometrie Differentielle Globale
	Chapitre 0. Premiers elements de la Theorie des diffusions
		1. Le Balayage de Poincare
		2. Esperance conditionnelle
		3. Egalite d\'energie,temps d\'arrêt et convergence des martingales
		4. Passage à une variete riemannienne
		5. Le mouvement brownien
		6. Calcul integral de Ito
		7. Equations integrales stochastiques
	Chapitre I. Equations de comparaisons et diffusions
		1. Comparaison avec un problème en dimension 1
		2. Theorème de cornparaison en geometrie Riemannienne semi locale
		3. Estimees riemanniens globaux
		4. Passage du local au global
	Chapitre II. Annulations de cohomologie et proprietes ergodiques de la diffusion horizontale
		1. Formule de la moyenne pour les formes harmoniques
		2. Principe du maximum et calcul de pertubation
		3. Conclusion
		4. Cas des espaces homogènes
		5. Cohomologie relative des varietes à bord
		6. Cas de fibres localement plats
	Chapitre III. Formules de Poisson
		1. Demonstration d\'une conjecture de Bremerman
		2. Une formule de Poisson sur le demi-plan de Siegel de rang 2
	Appendice
	References
Solvability of Invariant Differential Operators on Homogeneous Manipolds
	1. Introduction and summary
	2. Solvability results. Indications of proofs
	Bibliography