Table of contents

CONTENTS Introduction § 1. Abstract parabolic operators § 2. G-convergence of abstract parabolic operators. The compactness theorem § 3. G-convergence of parabolic differential operators. Auxiliary results § 4. Basic properties of the G-convergence of parabolic differential operators § 5. Estimates for the coefficients of a G-limiting operator. Some examples References

CONTENTS Introduction § 1. Homology theory § 2. Local duality § 3. Supports and covers § 4. Global duality § 5. Holomorphically complete spaces § 6. Dualizing complexes References

CONTENTS Introduction Chapter I. Conditions for absolutely-representing systems § 1. Conditions in projective and inductive limits of Banach spaces § 2. Conditions in certain function spaces § 3. The construction of specific representing systems on the basis of a general condition Chapter II. Properties of representing systems § 1. The defining Mittag-Leffler systems § 2. Extension of representing systems § 3. Stability of representing systems under the passage to a limit § 4. Representative subspaces and effective representing systems Chapter III. Representing systems and non-trivial expansions of zero § 1. Non-trivial expansions of zero in terms of a Mittag-Leffler system § 2. Construction of representing systems by the method of nearness Conclusion References

CONTENTS Introduction Chapter I. The theorem on holomorphic calculus (beginning) § 1. Taylor's joint spectrum § 2. The main theorem; two formulations of it and plan of the proof Remarks Chapter II. Elements of "locally convex" homological algebra § 0. Tensor products of modules and other preparatory material § 1. Complexes and the homology functor. Bicomplexes § 2. Projective modules and resolutions. The Koszul resolution § 3. Derived functors. The spaces Tor for modules and complexes Remarks Chapter III. The theorem on holomorphic calculus (continuation and end) § 1. Extension of the actions and the domination condition § 2. Analytically parametrized complexes. The connection between their exactness "in the large" and "on the fibres" § 3. Construction of the dominating complex. End of the proof Remarks Appendix. Extension of the actions and the role of torsion-(Tor-) preserving homomorphisms. Homorphisms of this class in general functional calculus and holomorphic calculus; the case of domains of holomorphy References