Titlebook: Elliptic Boundary Problems for Dirac Operators; Bernhelm Boo?-Bavnbek,Krzysztof P. Wojciechowski Book 1993 Springer Science+Business Media

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Mathematical Olympiad ChallengesWe explain the relative index theorem of Cheeger, Gromov & Lawson and offer an analytical interpretation which also works in the odd-dimensional case. We also give a simple proof of a special case of the excision principle for indices.

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Hermitian Operators and Unitary OperatorsThe establishing of the Calderón projector for Dirac operators over compact manifolds with boundary is rounded off by showing that all elements of ker.(., .), even the distributional solutions, have well-defined traces (boundary values).

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Ordinary Differential Equations,The spectral flow is investigated for families of self-adjoint elliptic operators with non-vanishing symbol class over an oriented closed smooth manifold.