On Expansions Over Harmonic Polynomial Products inR3.

Autor: Vakulenko, A. F.
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Zdroj: Journal of Mathematical Sciences; Aug2024, Vol. 283 Issue 4, p516-521, 6p
Abstrakt: In inverse problems, an important role is played by the following fact: the functions of the form ∑ k = 1 n f k x , y , z g k x , y , z , where fk, gk are the solutions of a second order elliptic equation in a bounded domain Ω ⊂ R 3 , constitute a dense set in L2(Ω). This paper deals with the Laplace equation. We show that the density does hold if fk and gk are harmonic polynomials, whereas the factors gk are invariant with respect to shifts or rotations. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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