This article is cited in 2 papers

On approximation of curves by level curves of homogeneous polynomials, and on series in homogeneous polynomials

È. È. Shnol'


Abstract: Conditions are found that are necessary and sufficient for a curve $r=R(\varphi)$ to bound the domain of convergence of a series $\sum P_n(x_1,x_2)$ in homogeneous polynomials. The conditions have a nonlocal character and can be expressed in terms of the Fourier coefficients of the Fourier coefficients of $R(\varphi)$.

UDC: 517.521

MSC: Primary 41A10, 40A05; Secondary 26C99, 34D05

Received: 13.03.1990

 English version: Mathematics of the USSR-Sbornik, 1992, 72:2, 403–411

Bibliographic databases:

• 
• 
• 
•