Complexes of Differential Operators

Complexes of Differential Operators

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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.
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Product details

  • Hardback | 416 pages
  • Dordrecht, Netherlands, United States
  • English
  • bibliography, indexes
  • 0792337069
  • 9780792337065

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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