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Boundary Value Problems With Global Projection Conditions

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2019 | ISBN-10: 3319701134 | 336 pages | PDF | 4 MB

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This book presents boundary value problems for arbitrary elliptic pseudo-differential operators on a smooth compact manifold with boundary. Every such operator admits global projection boundary conditions, giving rise to analogues of Toeplitz operators in subspaces of Sobolev spaces on the boundary associated with pseudo-differential projections. The book describes how these operator classes form algebras, and establishes the concept for Boutet de Monvel's calculus as well as for operators on manifolds with edge, including the case of operators without the transmission property. Further, the text shows how the calculus contains parametrices of elliptic elements. Finally, natural relations to the ellipticity of Atiyah-Patodi-Singer type for Dirac and other geometric operators, in particular spectral boundary conditions with Calderón-Seeley projections and characterization of Cauchy data spaces, are described.

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