Clifford algebras and the double-layer potential operator
[For the entire collection see Zbl 0742.00067.]For the purpose of providing a comprehensive model for the physical world, the authors set up the notion of a Clifford manifold which, as mentioned below, admits the usual tensor structure and at the same time a spin structure. One considers the spin space generated by a Clifford algebra, namely, the vector space spanned by an orthonormal basis satisfying the condition , where denotes the unit scalar of the algebra and () the nonsingular Minkowski...
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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.
This is an exposition of a general machinery developed by M. G. Eastwood, T. N. Bailey, C. R. Graham which analyses some real integral transforms using complex methods. The machinery deals with double fibrations complex manifold; totally real, real-analytic submanifold;...
This contribution shows how to compute upper bounds of the optimal constant in Friedrichs’ and similar inequalities. The approach is based on the method of [9]. However, this method requires trial and test functions with continuous second derivatives. We show how to avoid this requirement and how to compute the bounds on Friedrichs’ constant using standard finite element methods. This approach is quite general and allows variable coefficients and mixed boundary conditions. We use the computed...