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Conditions for reconstruction of multivariate homogeneous polynomials from sets of sample values are introduced. In addition, it is shown that one can explicitly obtain the polynomial coefficients from the sample data by considering frames for spaces of symmetric tensors. Further, it is discussed how the reconstruction of homogeneous polynomials can be used to approximate certain smooth functions.doi:10.1515/apam-2012-0028 fatcat:pxmdxdkxczc2jnab5fnv4tpg44