Geodesic
On Representations of Algebraic Polynomials by Superpositions of Plane Waves
Serdica Mathematical Journal, Tome 28 (2002) no. 4, pp. 379-390.

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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 .
Keywords: Non-Linear Approximation, Polynomials, Plane Waves, Ridge Functions, Chebyshev-Fourier Analysis 
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     title = {On {Representations} of {Algebraic} {Polynomials} by {Superpositions} of {Plane} {Waves}},
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Oskolkov, K. On Representations of Algebraic Polynomials by Superpositions of Plane Waves. Serdica Mathematical Journal, Tome 28 (2002) no. 4, pp. 379-390. http://geodesic.mathdoc.fr/item/SMJ2_2002_28_4_a7/