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A symbolic calculus for layer potentials on $ C\sp 1$ curves and $ C\sp 1$ curvilinear polygons

Author: Jeff E. Lewis
Journal: Proc. Amer. Math. Soc. 112 (1991), 419-427
MSC: Primary 47G30; Secondary 35S05, 45E05, 47A53, 47G10
MathSciNet review: 1043413
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Abstract: A symbolic calculus for some algebras of Mellin operators on the finite interval $ J \equiv \left[ {0,1} \right]$ is developed. The algebras are ample enough to include singular integral operators and analytic double layer potentials and their adjoints on $ {C^1}$ curves and piecewise $ {C^1}$ curves with corners. Fredholmness and the index of the operators on $ {L^p}\left( J \right)$ are completely determined by the principal symbol on $ {L^p}\left( J \right),{\text{Smb}}{{\text{l}}^{1/p}}$.

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Additional Information

Keywords: Layer potentials, Mellin operators, nonsmooth domains, pseudodifferential operators, symbolic calculus
Article copyright: © Copyright 1991 American Mathematical Society

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