It is proved that a bounded linear translation invariant operator on L 2 (R d ) satisfies the Bedrosian theorem if and only if it is a linear combination of the compositions of the partial Hilbert transforms and the identity operator. This observation justifies a definition of multidimensional analytic signals in the papers [T. Bulow, G. Sommer, Hypercomplex signals-a novel extension of the analytic signal to the multidimensional case, IEEE Trans. Signal Process. 49 (2001) 2844-2852] and [S.L. Hahn, Multidimensional complex signals with single-orthant spectra, Proc. IEEE 80 (1992) 1287-1300].

R. M. Brown's theorem on mixed Dirichlet and Neumann boundary conditions is extended in two ways for the special case of polyhedral domains. A (1) more general partition of the boundary into Dirichlet and Neumann sets is used on (2) manifold boundaries that are not locally given as the graphs of functions. Examples are constructed to illustrate necessity and other implications of the geometric hypotheses.

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