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Calculus on a Manifold with Edge and Boundary

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Abstract

We study elements of the calculus of boundary value problems in a variant of Boutet de Monvel’s algebra (Acta Math 126:11–51, 1971) on a manifold N with edge and boundary. If the boundary is empty then the approach corresponds to Schulze (Symposium on partial differential equations (Holzhau, 1988), BSB Teubner, Leipzig, 1989) and other papers from the subsequent development. For non-trivial boundary we study Mellin-edge quantizations and compositions within the structure in terms a new Mellin-edge quantization, compared with a more traditional technique. Similar structures in the closed case have been studied in Gil et al. (Osaka J Math 37:221–260, 2000).

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  1. Institute of Mathematics, University of Potsdam, 14476, Potsdam, Germany

    S. Khalil & B.-W. Schulze

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  1. S. Khalil
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  2. B.-W. Schulze
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Correspondence to S. Khalil.

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Communicated by Daniel Aron Alpay.

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Khalil, S., Schulze, BW. Calculus on a Manifold with Edge and Boundary. Complex Anal. Oper. Theory 13, 2627–2670 (2019). https://doi.org/10.1007/s11785-018-0800-y

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