Constrained Approximation and Interpolation in Hilbert Function Spaces

are ofimportance in systems and control and certain identification problems arenaturally solved by optimization 1, 17, 25 . Then again, the study ofwxinverse 2D Dirichlet]Neumann problems leads naturally to questions ofharmonic approximation 4 . A third example is to be found in signalwxprocessing 10, 17 where the Paleywx ]Wiener spaces are of crucial impor-tance and again certain sampling problems can be expressed in terms ofHilbert space optimization.We consider here a family of bounded extremal problems and ofinterpolation problems expressed using two distinct orthogonal decomposi-tions of some Hilbert space

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