ELLIPTIC SINGULAR INTEGRO-DIFFERENTIAL OPERATORS

Abstract

CONTENTS Introduction § 1. Theme of the article § 2. Brief survey of the literature Chapter I. Function spaces § 3. Notation and terminology § 4. The spaces § 5. The spaces Chapter II. Singular integro-differential operators § 6. Expansion in terms of spherical functions § 7. Singular integral operators in § 8. Singular integro-differential operators in and on a manifold without boundary § 9. Singular integro-differential operators in a half-space and on a manifold with boundary Chapter III. Elliptic operators on a manifold without boundary § 10. Relation of the Noether property with regularizers and an a priori estimate § 11. Elliptic operators in § 12. Elliptic operators on a manifold without boundary Chapter IV. Elliptic boundary-value problems on a manifold with boundary § 13. Definitions. The Shapiro-Lopatinskii condition § 14. Elliptic problems in . A priori estimate § 15. Elliptic problems in . Right quasi-regularizer § 16. Ellipticity and the Noether property on a manifold with boundary § 17. Some theorems on the index § 18. The Dirichlet problem References