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On representations of algebraic polynomials by superpositions of plane waves

A 2002 Preprint by K. Oskolkov

  • 2002:17
  • Let P be a bi-variate algebraic polynomial of degree n with the real senior part, and $Y=\{y _ j\} _ 1^n$ an n-element collection of pairwise non-colinear unit vectors on the real plane. It is proved that there exists a rigid rotation $Y^\varphi$ of Y by an angle $\varphi=\varphi(P,Y)\in[0,\frac{\pi}{n}]$ such that P equals the sum of n plane wave polynomials, that propagate in the directions $\in{Y^\varphi}$.

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