Complexes of differential operators
Author(s)
Bibliographic Information
Complexes of differential operators
（Mathematics and its applications, v. 340）
Kluwer Academic Publishers, c1995
- Other Title
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Metod parametriksa v teorii different︠s︡ialʹnykh kompleksov
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Note
Includes bibliographical references and indexes
"This is a completely revised and updated translation from the Russian original work Parametrix methods in the theory of differential complexes, Novobirsk, Nauka c1990" -- T.p. verso
Description and Table of Contents
Description
The main topic of this work is the study of general complexes of differential operators between sections of vector bundles. Although the global situation and the local one are often similar in content, the invariant language permits the simplification of the notation and more clearly reveals the algebraic structure of some questions. Recent developments in the theory of complexes of differential operators are dealt with to some degree: formal theory; existence theory; global solvability problem; overdetermined boundary problems; generalized Lefschetz theory of fixed points; and qualitative theory of solutions of overdetermined systems. Considerable attention is paid to the theory of functions of several complex variables. Examples and exercises are included.
Table of Contents
1. Resolution of differential operators. 2. Parametrices and fundamental solutions of differential complexes.3. Sokhotskii-Plemelj formulas for elliptic complexes. 4. Boundary problems for differential complexes. 5. Duality theory for cohmologies of differential complexes. 6. The Atiyah-Bott-Lefschetz theorem on fixed points for elliptic complexes.
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