The paper Is Sound Field Control Determined at all Frequencies? How is it Related to Numerical Acoustics? published by Franz Zotter and Sascha Spors at the 52nd International Conference of the Audio Engineering Society reviews the physical foundations of Sound Field Synthesis. The presentation given by Sascha Spors can be viewed here.
The paper shows how synthesis can be achieved using the equivalent scattering approach and the inherent problem of non-uniqueness is discussed. It is furthermore highlighted that the problem of synthesizing a sound field is directly related to the Boundary Element Method (BEM) used in numerical acoustics. It is finally derived that Wave Field Synthesis (WFS) can be interpreted as high-frequency approximation of the exact solution.