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Get Access to Full TextConditions 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.
Keywords: Frames; homogeneous polynomials; sampling; symmetric tensors
Received: 2012-09-22
Accepted: 2013-01-04
Published Online: 2013-02-01
Published in Print: 2013-02-01
Citation Information: Advances in Pure and Applied Mathematics, Volume 3, Issue 4, Pages 421–441, ISSN (Online) 1869-6090, ISSN (Print) 1867-1152, DOI: https://doi.org/10.1515/apam-2012-0028.
© 2013 by Walter de Gruyter Berlin Boston.
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