# On Representations of Algebraic Polynomials by Superpositions of Plane Waves

Serdica Mathematical Journal (2002)

- Volume: 28, Issue: 4, page 379-390
- ISSN: 1310-6600

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topOskolkov, 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 -

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