On Representations of Algebraic Polynomials by Superpositions of Plane Waves

Oskolkov, K.. "On Representations of Algebraic Polynomials by Superpositions of Plane Waves." Serdica Mathematical Journal 28.4 (2002): 379-390. <http://eudml.org/doc/11570>.

@article{Oskolkov2002,
abstract = {* The author was supported by NSF Grant No. DMS 9706883.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 .},
author = {Oskolkov, K.},
journal = {Serdica Mathematical Journal},
keywords = {Non-Linear Approximation; Polynomials; Plane Waves; Ridge Functions; Chebyshev-Fourier Analysis; nonlinear approximation; ridge functions; polynomials},
language = {eng},
number = {4},
pages = {379-390},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {On Representations of Algebraic Polynomials by Superpositions of Plane Waves},
url = {http://eudml.org/doc/11570},
volume = {28},
year = {2002},
}

TY - JOUR
AU - Oskolkov, K.
TI - On Representations of Algebraic Polynomials by Superpositions of Plane Waves
JO - Serdica Mathematical Journal
PY - 2002
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 28
IS - 4
SP - 379
EP - 390
AB - * The author was supported by NSF Grant No. DMS 9706883.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 .
LA - eng
KW - Non-Linear Approximation; Polynomials; Plane Waves; Ridge Functions; Chebyshev-Fourier Analysis; nonlinear approximation; ridge functions; polynomials
UR - http://eudml.org/doc/11570
ER -