Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/512

 Title: On Representations of Algebraic Polynomials by Superpositions of Plane Waves Authors: Oskolkov, K. Keywords: Non-Linear ApproximationPolynomialsPlane WavesRidge FunctionsChebyshev-Fourier Analysis Issue Date: 2002 Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences Citation: Serdica Mathematical Journal, Vol. 28, No 4, (2002), 379p-390p Abstract: Let P be a bi-variate algebraic polynomial of degree n with the real senior part, and Y = {yj }1,n an n-element collection of pairwise noncolinear unit vectors on the real plane. It is proved that there exists a rigid rotation Y^φ of Y by an angle φ = φ(P, Y ) ∈ [0, π/n] such that P equals the sum of n plane wave polynomials, that propagate in the directions ∈ Y^φ . Description: * The author was supported by NSF Grant No. DMS 9706883. URI: http://hdl.handle.net/10525/512 ISSN: 1310-6600 Appears in Collections: Volume 28 Number 4

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