The Atiyah-Patodi-Singer theorem for perturbed Dirac operators on even-dimensional manifolds with bounded geometry.
Fox, Jeffrey, Haskell, Peter (2005)
The New York Journal of Mathematics [electronic only]
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Fox, Jeffrey, Haskell, Peter (2005)
The New York Journal of Mathematics [electronic only]
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Bunke, Ulrich
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The author introduces boundary conditions for Dirac operators giving selfadjoint extensions such that the Hamiltonians define elliptic operators. Using finite propagation speed methods and assuming bounded geometry he estimates the trace of the difference of two heat operators associated to a pair of Dirac operators coinciding on cocompact sets.
Gorm Salomonsen (1998)
Journées équations aux dérivées partielles
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I present an alternative way of computing the index of a Dirac operator on a manifold with boundary and a special family of pseudodifferential boundary conditions. The local version of this index theorem contains a number of divergence terms in the interior, which are higher order heat kernel invariants. I will present a way of associating boundary terms to those divergence terms, which are rather local of nature.
Gonzalo E. Reyes (2007)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Nazaikinskii, V.E., Sternin, B.Yu. (2006)
Abstract and Applied Analysis
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Bernhelm Booss, Bert Schulze (1983)
Banach Center Publications
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Dagmar Medková (1998)
Applications of Mathematics
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For open sets with a piecewise smooth boundary it is shown that we can express a solution of the Robin problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series.