A symbolic calculus for layer potentials on 𝐶¹ curves and 𝐶¹ curvilinear polygons

Lewis, Jeff E.

doi:10.1090/S0002-9939-1991-1043413-4

A symbolic calculus for layer potentials on $C^ 1$ curves and $C^ 1$ curvilinear polygons
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by Jeff E. Lewis

Proc. Amer. Math. Soc. 112 (1991), 419-427

DOI: https://doi.org/10.1090/S0002-9939-1991-1043413-4

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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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Potential techniques for boundary value problems on

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