On a New Positive Extension Problem for Block Toeplitz Matrices
We consider positive extension problems for block Toeplitz matrices when the specified entries form a stalactite type pattern. These problems do not seem in general to be amenable to the classical methods (they correspond to bitangential interpolation problems in the class of Carathéodory functions of a kind usually not solvable by the classical methods of interpolation). We solve these problems by reduction to a tangential interpolation with symmetries in a Carathéodory class.
D. Alpay, V. Bolotnikov and Ph. Loubaton. On a new positive extension problem for block Toeplitz matrices. Linear Algebra and its Applications, vol. 268 (1998) pp 247-287.