Convolution type operators with symmetry appear naturally in boundary value problems for elliptic PDEs in symmetric or symmetrizable domains. They are defined as truncations of translation invariant operators in a scale of Sobolev-like spaces that are convolutionally similar to subspaces of even or odd functionals. The present class, as a basic example, is closely related to the Helmholtz equation in a quadrant, where a possible solution is "symmetrically" extended to a half-plane. Explicit factorization methods allow the representation of resolvent operators in closed analytic form for a large class of boundary conditions including the two-impedance and the oblique derivative problems. Moreover they allow fine results on the regularity and asymptotic behavior of the solutions.
CITATION STYLE
De Castro, L. P., & Speck, F. O. (2017). Convolution type operators with symmetry in bessel potential spaces. Operator Theory: Advances and Applications, 258, 21–49. https://doi.org/10.1007/978-3-319-47079-5_2
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