## 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 $\in{Y^\varphi}$.