Mergelyan's theorem on polynomial approximation
Teorema de Mergelián de aproximación por polinomios
- Date
- 1951 · confidence high
- Place
- Moscow, Russia
- Credited to
- Sergey Mergelyan
- Field
- Knowledge & symbols
What was discovered
A theorem characterising which functions can be uniformly approximated by polynomials on a compact set in the complex plane: those continuous on the set and holomorphic in its interior, if the complement is connected. It solved a problem open since Weierstrass, Runge and Walsh.
Mergelyan, an Armenian born in Simferopol, proved it at 23 at the Steklov Institute; the result was published in 1951-1952.
What it led to
- development of complex analysis and approximation theory
- closing the line of work of Runge and Walsh
- Mergelyan later became director of the Yerevan Computing Centre (1960)