Solutions to P(i∇)u=0 are exactly the multi-layer distributions of order ≤N on S^{d-1}, or satisfy a higher-order Laplace equation under flatness.
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A generalized Liouville theorem via division
Solutions to P(i∇)u=0 are exactly the multi-layer distributions of order ≤N on S^{d-1}, or satisfy a higher-order Laplace equation under flatness.