## On one question of Ed Saff

Boris Shekhtman

### Abstract

In relation to Fourier-Padé approximation, Ed Saff observed that Taylor and Lagrange interpolation projections satisfy the following property: $$P(f)\cdot P(g)\in \Pi _{n}\Longrightarrow P(f\cdot g)=P(f)\cdot P(g).$$ We classify all projections that satisfy this property, thus answering a question of Saff. Some error formulas for approximation with the above-mentioned projections are also produced.

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### Key words

ideal projection, Hermite interpolation, error formula

### AMS subject classifications

41A05, 41A10, 41A45, 41A80

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