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On Boundary Value Problems for Dirac Type Operators: I. Regularity and Self-Adjointness

✍ Scribed by Jochen Brüning; Matthias Lesch

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
371 KB
Volume
185
Category
Article
ISSN
0022-1236

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✦ Synopsis

In a series of papers, we will develop systematically the basic spectral theory of (self-adjoint) boundary value problems for operators of Dirac type. We begin in this paper with the characterization of (self-adjoint) boundary conditions with optimal regularity, for which we will derive the heat asymptotics and index theorems in subsequent publications. Along with a number of new results, we -extend and simplify the proofs of many known theorems. Our point of departure is the simple structure which is displayed by Dirac type operators near the boundary. Thus our proofs are given in an abstract functional analytic setting, generalizing considerably the framework of compact manifolds with boundary. The results of this paper have been announced previously by the authors (

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