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Title: On Representations of Algebraic Polynomials by Superpositions of Plane Waves
Authors: Oskolkov, K.
Keywords: Non-Linear Approximation
Plane Waves
Ridge Functions
Chebyshev-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.
ISSN: 1310-6600
Appears in Collections:Volume 28 Number 4

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