Characterization of Generalized Haar Spaces Original Research Article

We say that a subsetGofC0(T, Rk) is rotation-invariant if {Qg: g∈G{=Gfor anyk×korthogonal matrixQ. LetGbe a rotation-invariant finite-dimensional subspace ofC0(T, Rk) on a connected, locally compact, metric spaceT. We prove thatGis a generalized Haar subspace if and only ifPG(f) is strongly unique of order 2 wheneverPG(f) is a singleton.